Therefore, to construct a 120º angle, construct a 60º angle and then extend one of its arms as shown below. how to use an angle bisector to construct some angles for example, 90 degrees, 45 degrees, 60 degrees, 30 degrees, 120 degrees, 135 degrees, 15 degrees. The angle APT formed measures 90°. Sides ABD and AC are equal. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. 100. Thus, the angle sum of the triangle ABC = 60° + 55° + 65° = 180°. As long as they add up to 90° they will be known as complementary angles. 300 seconds . Are the triangles congruent? The radian measure of an angle whose terminal side is along the negative x-axis is . The angle is the amount of turn between each arm. These kinds of minutes and seconds are like the ones on a clock — a minute is bigger than a second. are special types of quadrilaterals with some of their sides and angles being equal. We can construct a 90º angle either by bisecting a straight angle or using the following steps. The roofs of many houses are supported by a set of congruent triangular braces known as trusses. An acute angle is the smallest angle measuring between 0 to 90 degrees, whereas the obtuse angle measures between 90 and 180 degrees. Taking O as center and any radius, draw an arc cutting OA at B. The angle APT formed measures 90°. 1. Step 1: In order to construct an angle of 30°, we first need to construct an angle of 60° and then further bisect it. This arc must cut the arc which is drawn in the above step at a point R. Step 4: Now place the point of the compass at R and draw an arc of the radius which is similar to the radius of PQ in order to cut the arc which is drawn at step 2 at another point S. Step 5: With the point of the compass at R, draw another arc of radius the same as the radius of PQ near the point T as shown in the figure below. Tags: Question 7 . Protractors are widely used in schools to help students learn geometry. how to construct an angle bisector of a given angle. Vertical angles: Angles that … Construct a 90° angle and bisect it. arrow_back Construction Of Angles Measuring 30, 45, 60, 75, 90 and 105 degrees Using Set Squares. Cloudflare Ray ID: 6161944f795d2c8a [20 pts) 6) Using only compass and straightedge construct Angles with the following measures: a) 45 degrees b) 30 degree c the medians of the following triangle e) the incenter of the following … is a straight line that divides the angle into two equal parts. Construct the angles of the following measurements: (i) 30° (ii) 22 1 2 ° (iii) 15° 4. Protractor. Then place the point of the compass and then draw an arc which passes through Q. View solution. If two angles add up to measure 90° then they are known as complementary angles. Yes. Constructing a 90º Angle. Direct students to use the inner scale if the angle opens to the right, and the outer scale if the angle opens to the left, so they can easily measure the angles. Let’s begin with learning to draw an angle using a protractor, and also learn how to measure already drawn angles. Join OE Thus, ∠ AOE = 30° Ex 11.1, 3 Construct the angles of the following measurements : 221/2° 221/2 = 45/2 So, we make 45° and then make its bisector Steps of construction Draw a ray OA. Q. Q. Congruent angles are denoted as $$\angle A\cong \angle B$$ Or could be shown by an arc on the figure to indicate which angles that are congruent. Supports, like trusses, usually involve triangles because triangles are rigid. So think of a degree like an hour, and you’ve got it down: One degree equals 60 minutes. The following are supplementary angles. Actually, it’s just a pinch. Step 2: Now place the point of the compass at P and then draw an arc which cuts the arm at Q. A 45˚ angle can be obtained by bisecting a 90˚ angle. Then measure the angles to the nearest 5 degrees using a protractor and record these measurements on your paper. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. 30 seconds . 9th - 12th grade. Additionally, we’ll also teach you to draw or measure angles more than 180° using a regular semicircular protractor. We can use the angle bisector to construct some other angles from existing angles. And from the constructed angles, (that are multiples of 15), it is easy to bisect them (without a protractor). Using the properties of a rhombus it can be shown that the angle created has a measure of 30 degrees. Using your compass, measure the length of . In this section, you will learn how to construct angles using ruler and compass. Construct, not measure. View solution. twice the radius of the inscribed circle). Measuring Angles with 5-Degree Increments | Inner & Outer Scale. 1. Sum of the angles in a triangle is 180 degree worksheet. Now use compass and open it to any convenient radius. Step I: Draw the given ray PQ. Angle 1 and angle 2 are complementary angles because together they form a right angle. To be able to speak about angles that measure less than $$1^\circ$$, we use submultiples of a degree, so we avoid working with expressions like the following: This angle measures half a degree; This angle measures $$0,76$$ degrees; Thus, the sexagesimal degree has … Construct the angles of the following measurements: I)\(30^\circ\) II) \(22(1/2)^\circ\) III)\(15^\circ\) Answer : I) Steps of construction: 1. Vedantu academic counsellor will be calling you shortly for your Online Counselling session. Step 1 : Draw a line ‘l’ and mark a point ‘O’ on it. What is the measure of the unlabeled angle of the triangle? Pro Subscription, JEE On one set of axes draw angles of the following radian measures: On one set of axes draw angles of the following radian measures: (HINT: Find a common denominator) 6.1.10 and 6.1.13 Draw each angle in standard position and state the quadrant in which the terminal side of the angle lies or the axis on which the terminal side of the angle lies. Now with the point of the compass at R, draw another arc in order to cut the arc drawn at step 5 at T. Now join the point T to the point P. Now the angle QPT is 30°. Step II: Draw OC, the bisector of ∠AOB. Angles can be measured using the inner or outer scale of the protractor. How To Construct A 30 Degree Angle A 30° 30 ° angle is half of a 60° 60 ° angle. Log in. It’s the adorable angle. Step 1 : Draw a line segment BC of length 3.4cm Step 2 : Draw an angle of 45 degree from point B Step 3 : From Ray AX cut off the line segment BD = 1.5cm Step 2: Draw the arm PQ Dear Student, 30 ° The below given steps will be followed to construct an angle of 30… ... Construct long stretches of highway and railroad. (b) Convert to degree measure. This angle measures 60° as the triangle PQR formed is an equilateral triangle. This construction works by creating an equilateral triangle. Again use compass and open it to any convenient radius. 3. Construct an angle of 90° at the initial point of a given ray and juste the construction. Likewise, an angle of size 1° has radian measure /180. (as shown below) 3). 1. Now use a compass to construct a 60° angle at point A. This arc must cut the arc which is drawn in the above step at a point R. Now place the point of the compass at R and draw an arc of the radius which is similar to the radius of PQ in order to cut the arc which is drawn at step 2 at another point S. With the point of the compass at R, draw another arc of radius the same as the radius of PQ near the point T as shown in the figure below. SURVEY . To construct an angle using protractor, we must need the following mathematical instruments. )Bisect the angle this way: Strike an arc through both legs of the 90° angle. When we construct, or draw, geometric figures, we often need to bisect lines or angles.Bisectmeans to cut something into two equal parts. The degree measure of angle A of isosceles triangle ABC is 30 degrees. Similar? By combining them you can construct other angles. Protractor. Example: A 30˚ angle can be obtained by bisecting a 60˚ angle. When measuring from a line: a positive angle goes counterclockwise (opposite direction that clocks go) a negative angle goes clockwise; Example: −67° Parts of an Angle. Understanding the basics of this is very important and thus one must try and learn this properly. Constructing 75° 105° 120° 135° 150° angles and more. 120° angle can be constructed using the logic that 60° + 120° = 180°. To construct an angle, we must need the following mathematical instruments. Most calculators can be set to use angles measured with either degrees or radians. Constructing Angles Using Protractor - Examples. (i) 30 ° The below given steps will be followed to construct an angle of 30°. 60. Special line segments in triangles worksheet. Step 1: In order to construct an angle of 30°, we first need to construct an angle of 60° and then further bisect it. 90* 82* 98* 75* Tags: Question 8 . The angle ∠AOC so obtained is the required angle of measure 45º. Share 0. Construct the following angles and verify by measuring them by a protractor: (i) 75° (ii) 105° (iii) 135° 5. This means that 120º is the supplement of 60º. 90* 82* 98* 75* Tags: Question 8 . The corner point of an angle is called the vertex. However, squares, rectangles, etc. Construct an equilateral triangle, given its side and justify the construction. It is easy to convert between degree measurement and radian measurement. From each point of intersection (of the arc and legs), strike arcs of the same radius such that they intersect each other. 2) Triangle construction, when its base, difference of the other two sides and one base angle are given. Two angles whose measures together are 180° are called supplementary e.g. Ruler. Report an issue . And let me move the protractor out of the way so we can get a good look at it. An angle bisector. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. Step 6: Now with the point of the compass at R, draw another arc in order to cut the arc drawn at step 5 at T. Step 7: Now join the point T to the point P. Now the angle QPT is 30°. Pro Lite, Vedantu First, follow the steps above to construct your 60° 60 ° angle. 2.Taking D and E as centres and with the radius more than 1/2 DE, draw arcs to intersect each other, say at F. 3.Draw the ray XF. And I want to give credit to the person who built this protractor, because I think it's pretty neat. Build a square around the circle and construct the octagon from that. Construct angles that measure the given number of degrees. And we got it wrong. (v) Construction of An Angle of 120º 90. a. We use one of those angles to get the desired 60 degree result. Draw ∠BXA = 110° with the help of a protractor. Now, for the next part, we can use a protractor to find the rest of the angles. Construct a triangle ABC in which BC = 3.4 cm , AB - AC = 1.5 cm and ∠B = 45 0. SURVEY . We now can easily obtain a formula to convert from degrees to radians and vice-versa. Etc. We can measure Angles in Degrees. Related Topics: More Geometry Lessons. Taking P as centre and with some radius, draw an arc of a circle which intersects PQ at R. Step II: Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point S. There are 360 degrees in one Full Rotation (one complete circle around). 60. Use the ruler to find C such that AC is 4.5 cm long. Example 1 : Construct an acute angle of 60 °. One of the most important aspects of geometry is constructing angles. One minute equals 60 seconds. So we can apply this knowledge to construct a 30° angle. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. With the point of the compass at S, draw an arc of radius similar to the radius of arc PQ and cut the arc which was drawn at step 5 at the point T. Join T to P using a scale. The triangle ABC formed is the required triangle. See the proof below for more on this. To construct an angle of 60 degrees, we need to draw first: (a) A ray (b) An arc (c) Two rays (d) A straight line. Select city Home Patna Ranchi Bhopal Lucknow Indore Raipur Allahabad Dehradun Varanasi. This page shows how to construct (draw) a 60 degree angle with compass and straightedge or ruler. Construct a regular octagon given the perpendicular distance from one side of the octagon to the opposite (i.e. Repeaters, Vedantu In an equilateral triangle, all the angles are equal and they are equal to 60° in size. There are different ways to bisect a line segment. So just like that. A 30-60-90 right triangle (literally pronounced "thirty sixty ninety") is a special type of right triangle where the three angles measure 30 degrees, 60 degrees, and 90 degrees. Often, we apply the following steps. So let's see what we-- oh, 155 degree angle, not 150 degree angle. The triangle is significant because the sides exist in an easy-to-remember ratio: 1:\(\sqrt{3}\):2. Example: Construct an angle bisector for the following angle: Step VII: Draw OB and produce it to C. ∠AOC is the angle of measure 90º. Example 1 : Construct an acute angle of 60 °. This page shows how to construct (draw) a 30 degree angle with compass and straightedge or ruler. Properties of triangle worksheet. Use ruler and draw a Line segment OB of any convenient length. 90. And the two straight sides are called arms. Step 4: Place the point of the compass at Q and then draw the arc which cuts the arc drawn at the above step at another point R. Step 5: WIth the compass at Q, draw another arc near the point T as shown in the figure. To do this, draw a line segment and label it . Taking Q and C as center , with radius more than 1/2QC, draw arcs intersecting at R. 9. Sorry!, This page is not available for now to bookmark. 11.3 Some Constructions of Triangles Now, we use the following steps for required construction . Adding angles. The problem as stated is impossible to solve for arbitrary angles, as proved by Pierre Wantzel in 1837. Draw an arc to indicate the angle that was measured. To construct a 30-degree angle, you first need to construct an equilateral triangle, which will have three 60-degree angles. A straight angle. It’s any angle that … Step 1:Draw a line segment. 5. Please enable Cookies and reload the page. Now place the point of the compass at P and then draw an arc which cuts the arm at Q. • Properties of a 30-60-90 Right Triangle A special kind of triangle. Complimentary angle can be adjacent angles. 65° c. 115° d. 135° e. 5° f. 175° g. 27° h. 117° i. (See the wikiHow article Construct a 90 Degrees Angle Using Compass and Ruler. To construct an angle, we must need the following mathematical instruments. 60 degree is one of the most basic constructions, which facilitates constructing angles of several other measures. Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website! Let's put the protractor here. Step 2: Place the point of the compass at P and draw an arc that passes through Q. This next exercise asks you to click on the radian measure of an angle given in degrees. Construct the angles of the following measurement at 30 degree - 1851611 1. 1.Taking X as centre and any radius daw an arc to Intersect the rays XA and XB, say at E and D, respectively. Construct the following angles and verify by measuring them by a protractor: 1 3 5 o. Tags: Question 7 . (as shown below) 2). To examine what this means, try the following activity. Join now. What is the measure of the unlabeled angle of the triangle? A quadrilateral, in general, has sides of different lengths and angles of different measures. A 15˚ angle can be obtained by bisecting a 30˚ angle. A Euclidean construction. Angles that measure 30°, 45°, 60°, 75°, 90° and 105° can be drawn using the pair of set squares in the geometry box. Two angles whose measures add to 90 degrees. The first one is by bisecting a straight angle and the other step is given below. Median response time is 34 minutes and may be longer for new subjects. two right angles are supplementary since 90° + 90° = 180°. To construct an angle using protractor, we must need the following mathematical instruments. Step 2: Now use a compass to construct a 60° angle at point A. The right angle is exactly equal to 90 degrees. Angles measuring 30 and 60 degrees. • Your IP: 46.101.36.144 example 1250 in Radians second input as a fraction of π: Example 27/5 π or 1.2 π then press the button "Find Quadrant" on the same row. View solution. is a straight line that divides the angle into two equal parts. 100. Step 1: First draw the line AB which is 6m long. For example 90° means 90 degrees. Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass.. Step 3:Place the compass pointer at P and mark an arc th… We can also have complementary angles that are not adjacent to each. The angles don't have to be adjacent to each other to be known as complementary. Compass. 1. In these lessons, we will learn how to construct a 30 degrees angle from a 60 degrees angle. Properties of parallelogram worksheet. Without changing the width of the compass, place your compass at Point P and draw an arc above Answer: (a) A ray Hint: To construct an angle of 60 degrees we need to start at the initial point of a ray. Most protractors measure angles in degrees, whereas a few also measure them in radians. An angle bisector. Apart from these, there are three other types such as straight, reflex and full rotation. Ask your question. One Degree. This is shown in Constructing the sum of angles. Now place the point of the compass at Q and draw an arc which has the radius similar to the radius of PQ. The given angle may be in degrees or radians. Hence, 1° equals π/180 radians. Measuring Angles | Inner & Outer Scale. Solution: We must find the degree measure of the other two angles of triangle ABC. 9). The perimeter is 12 units. How to Use a Protractor to Draw an Angle. SURVEY . On other pages there are instructions for constructing angles of 30°, 45°, 60° and 90°. Note that angle 1 and angle 2 do not have to be adjacent to be complementary as long as they add up to 90 degrees. Step 3: Now place the point of the compass at Q and draw an arc which has the radius similar to the radius of PQ. 2. And just to make sure that blue arc is measuring this angle right over here, not the outer one. Use a ruler and compass and construct a triangle ABC. Step 3: Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R. Step 4: With the point of the compass still at Q, draw an arc near T as shown. Join OP Thus, ∠ AOP = 90° and ∠ POD = 30° Now, we bisect ∠ POD i.e. 80. Sum and Difference of Angles in Trigonometry, Table of 90 - Multiplication Table of 90, Vedantu Ruler. And with O as center , draw an arc which cuts line segment OB at X . Thus, we can understand that in order to construct 120° we can construct 60° angle and then further extend one of its arms as shown below in the figure. 2. Constructing a 30° Angle: We know that 30° is half of 60°. Angle Types. And it's a pretty cool exercise because it has this little virtual protractor that we can use to actually measure angles. Step 5: With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T. Step 6: Join … Often you are required to construct some angles without using a protractor. 300 seconds . Step 3: Use the ruler to find C such that AC is 4.5 cm long. So, to draw a 30° 30 °, construct a 60° 60 ° angle and then bisect it. Find two others in the room who used your same angles and compare your triangles. Using ruler and compasses, construct the following angles: 3 0 o. answer choices . Construction Of Angles Measuring 30, 45, 60, 75, 90 and 105 degrees Using Set Squares . A Measure of Acute Angle = 360° – a Measure of Reflex Angle. Main & Advanced Repeaters, Vedantu Q. We know that 30° is half of 60°. Two angles with the same measure are called congruent angles. and 1 radian equals 180/π degrees. Drawing an angle using a protractor is very simple. Since ZB is a straight line, so formed Angle AOZ = 90 Degree (angle sum property) Now, to construct at 135 degree angle, we will construct the angle bisector of above angle AOB. Angles are most commonly measured by degrees, but for those of you who are sticklers for accuracy, even smaller units of measure can be used: minutes and seconds. 1. The steps are: 1. Performance & security by Cloudflare, Please complete the security check to access. Then we'll start getting into obtuse angles, 100, 110, 120, 130, 140, 150. Recall that an equilateral triangle has all three interior angles 60 degrees. Types of angles worksheet. The circumference of the entire circle is 2π, so it follows that 360° equals 2π radians. (30°)/2 = 15° 7. Then place the point of the compass at P and draw an arc such that it passes through Q. Answer. For (a)–(d), use the ray shown as one of the rays of the angle with its endpoint as the vertex of the angle. Take a look! A Euclidean construction. So we have this little angle tool here that we can use to construct an angle. 80. What are the sides? SURVEY . Construct the angles of the following measurements: I)\(30^\circ\) II) \(22(1/2)^\circ\) III)\(15^\circ\) rustudies. 30° b. I have a small part of it in this screen right over here. Proving trigonometric identities worksheet. … Since an angle of 2 has degree measure 360° it follows that an angle of 1 radian has degree measure (180/)°. It works by first creating a rhombus and then a diagonal of that rhombus. 2. 87. Find the measure of angle x. answer choices . in the triangle, AB = 5 cm, angle BAC = 60° and AC = 4.5 cm. Step 2: Then place the point of the compass at P and draw an arc such that it passes through Q. To construct 135 degree angle we first construct 90 degree angle and its steps of constructions are as follows: 1). krish456 krish456 26.11.2017 Math Secondary School Construct the angles of the following measurement at 30 degree 1 See answer krish456 is waiting for your help. Proving triangle congruence worksheet . (iv) Construction of An Angle of 45º Steps of Construction: Step I: Draw ∠AOB = 90º by following the steps given above. Positioning initial and terminal sides An […] And then they give us a protractor to actually measure the angle. 93. Positive and Negative Angles. What I have right in front of me is the Khan Academy measuring angles exercise. Join OR Thus, ∠ AOP = 90° and ∠ POD = 30° Now, we bisect ∠ POD … The sum of its interior angles is 360 degrees. Pro Lite, NEET In trigonometry and most other mathematical disciplines, you draw angles in a standard, universal position, so that mathematicians around the world are drawing and talking about the same thing. So let's set it up. Q: 12. Ruler. You may need to download version 2.0 now from the Chrome Web Store. Sol. Example 1 : Construct an acute angle of … Acute angle. Join now. 2. Building Construction: Basic Surveying DRAFT. (c) Label the reference angle in both degrees and radians. Example: Construct an angle bisector for the following angle: Step 6: With the point of the compass at S, draw an arc of radius similar to the radius of arc PQ and cut the arc which was drawn at step 5 at the point T. Step 7: Join T to P using a scale. Learn how to solve with the ratio of sides and angles of a triangle. Step 2:Take the compass and open it up to a convenient radius. Constructing Angles Using Protractor - Examples. Another way to prevent getting this page in the future is to use Privacy Pass. What is different? 96. We're asked to construct a 10 degree angle. See the proof below for more details. 138. For example, ∠ STA= 65 degrees and ∠ATR= 25 degrees are complementary angles that are adjacent. 4. Navigators, surveyors, and carpenters all use the same angle measures, but the angles start out in different positions or places. Construct the following using ruler and compass: angles of degree measure 30,45,75,105,135 Share with your friends. Thus, in order to draw 60°, we need to construct an equilateral triangle. This article teaches you how to draw a 90 degrees angle using a compass and a ruler. Semicircular protractor other pages there are three other types such as straight, reflex and full rotation ( complete. And ∠ATR= 25 degrees are complementary angles because together they form a right angle problem as stated impossible... Together are 180° are called congruent angles 120° = 180° 1 ) (... * Tags: Question 8 construction of angles measuring 30, 45, 60, 75, and... Use compass and straightedge or ruler and gives you temporary access to the web property measure /180 of angle. Protractors are widely used in schools to help students learn geometry this article teaches you how use. Available for now to bookmark us a protractor, we must find the measure! To examine what this means that 120º is the supplement of 60º equals... 120, 130, 140, 150 next exercise asks you to click on the radian /180! Angle ACB and calculate the angle angle = 360° – a measure of angle! Angle at point a of 30 degrees CAPTCHA proves you are a human and gives you temporary access the. 80 degrees, which most accurately measures long distances it to C. ∠AOC is amount. Angle or using the following mathematical instruments 90° angle, there are ways... Response time is 34 minutes and seconds are like the ones on a clock — minute... One degree equals 60 minutes an [ … ] a straight angle the! A side the circle and construct a 90° angle, construct the following steps: 10 ) are to... The radius similar to the web property line segment for arbitrary angles, 100, 110,,.!, this page shows how to construct a 60º angle and then a diagonal of that.! Complementary angles that are possible to draw an arc such that it passes through Q ratio::! 60º angle and the right end as point B produce it to any convenient radius line AB is! 140, 150 as they add up to measure but also to construct a semicircular. Tools such as straight, reflex and full rotation justify the construction then bisect.. Can be obtained by bisecting a 60˚ angle that … we 're asked to construct a degree. Then we 'll start getting into obtuse angles, as proved by Pierre Wantzel in 1837 {! Understanding the basics of this is shown in constructing the sum of the triangle is because... First one is by bisecting a straight angle and then draw an angle of the entire circle 2π. In one full rotation will learn how to construct an angle using protractor proves you are a human and you... Interior angles is 360 degrees in one full rotation be Set to use Privacy Pass Label it into equal! Verify by measuring them by a Set of congruent triangular braces known as complementary angles terminal., 130, 140, 150 next part, we must need the following angles verify! Both degrees and 60 degrees angle using compass and straightedge or ruler select city Home Patna Ranchi Bhopal Lucknow Raipur! Me is the protractor, which is a drawing tool that allows us only... Can put this solution on your website angle, there are 360 degrees ∠ POD = 30° now, use! Cm long angle BAC = 60° + 55° + 65° = 180° intersecting at R..! Draw a 30° 30 ° the below given steps will be followed to construct a degree... Two angles whose measures add to 180 degrees draw 60°, we must find rest. And any radius, draw an arc which meets the line OB at X and may be longer new. A 90° angle and more, angle BAC = 60° + 55° + 65° = 180° in... And radian measurement regular octagon given the perpendicular distance from one side of the triangle, all angles! In radians the Quadrant of an angle of 1 radian has degree measure 360° it follows an... Measure the angle into two equal parts, 110, 120,,... The roofs of many houses are supported by a protractor, because i think it 's neat. The most important aspects of geometry is constructing angles compass at P and draw an arc to indicate the this! To prevent getting this page shows how to construct an acute angle = 360° – a measure acute., 75, 90 and 105 degrees using Set Squares has the similar... A diagonal of that rhombus protractor and record these measurements on your paper base, difference the. Are construct the angles of the following measurements 30 degree types of quadrilaterals with some of their sides and angles the! Into two equal parts compass: angles of degree measure ( 180/ ) ° is than! This section, you will learn how to use Privacy Pass the bisector of ∠AOB protractors measure of. Measurement at 30 degree angle which we can apply this knowledge to construct 30...

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