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Constructing Angles

VSAT 2022

Why do We Need to Learn to Construct Angles?

One of the most significant components of geometry is the creation of angles, which is the "perfect" type of geometric construction. In geometry, the phrase construction refers to the precise sketching of forms, lines, or angles using mathematical instruments. In this tutorial, we will learn how to make angles with a protractor, compass, ruler, and pencil.


What is an Angle?

Before talking about constructing angles with a protractor, let us quickly reminisce about angles and their types.

  • An angle is made when two rays start from the same point or common point. This common point is known as the vertex of the angle and the two rays forming the angle are known as sides or arms.

  • On the basis of the inclination between its two arms, an angle can be obtuse (i.e. more than 90 degrees), acute (i.e. less than 90 degrees) or right-angled (i.e. exactly 90 degrees).

The construction of angles is a very crucial part of geometry because its knowledge is extended for the construction of other geometrical figures as well, for example, the triangles.


The Protractor and Its Uses

A protractor is a semi-circular disc that you can use to draw or measure angles. It has marks from 0 to 180-degree angles and can be used directly to measure any angle within the range. It has two sets of markings which are 0 to 180 degrees from left to right and vice versa.


How To Use a Protractor for Constructing Angles

For constructing angles of any measure whether it's acute, obtuse or a right-angle the easiest method is to use a protractor. Let us assume that you need to construct an angle of 160 degrees. Here are the steps.

  • Draw a line and name it BC.

  • Place the protractor with its point O on point B of the line segment BC.

  • Align OQ along the edge BC.

  • As we said earlier, the protractor has two-way markings. We will examine the scale which has 0 degrees near point C for this construction. Mark point A next to the 160 degrees mark on the scale.

  • Join points A and B. ∠ABC = 160 degrees is the required angle.

Constructing Angles of Unknown Measure

Constructing angles of unknown measures is quite fun and easy for it is like copying a given angle with unknown measurements. We achieve this task using compasses. Let us assume that you are given an acute angle ∠BAC that you are supposed to copy. Here are the steps:

  • Draw a line PQ and point P is the vertex of the duplicate angle.

  • Put your compass pointer at point A and develop a circular segment or arc that cuts arms AC and AB at points K and J separately.

  • Don't change the radius of the compass. Make an arc at PQ at point M.

  • Control the compass so that the pointer is set down at K and the pencil head is placed at J.

  • Keep the equal radius and then form an arc on the first arc while holding the compass pointer at M and mark the intersecting point as L.

  • Join the points P and L using a scale and extend the line up to R.

  • ∠RPQ is the needed angle.

How to Construct a 90-Degree Angle

Here we are explaining how to make a 90-degree angle with a compass and we have added the steps of construction of a 90-degree angle for your convenience:

Step 1: Take any ray OA.

Step 2: Let O be the centre and take any radius, draw an arc cutting OA at B.

Step 3: Take B as the centre and the same radius, and draw an arc cutting the first arc at C.

Step 4: Taking C as the centre and the same radius, make an arc intersecting again the first arc at D.

Step 5: Take C and D as the centre and keep radius as more than half of CD.

Step 6: Draw two arcs cutting each other at E then join OE.

Step 7: Here you have your desired angle ∠EOA = 90 degrees.

How to Construct a 75 Degree Angle

Here we are explaining how to make a 75-degree angle with a compass and we have added the steps of construction of 75-degree angle for your convenience.

Step 1: Take a look at OA.

Step 2: Using O as the centre and any appropriate radius, draw an arc that cuts OA at C.

Step 3: Using C as the centre and the same radius, cut the first arc at M.

Step 4: Using M as the centre and the same radius, cut off an arc that intersects the first arc at L.

Step 5: Using L and M as the centre and radius of more than half of LM, draw two arcs intersecting at B and joining OB at 90°.

Step 6: Now, with N and M as the centres, draw two arcs that intersect at P.

Step 7: Lastly, join OP.

Step 8: Angle POA is your required angle and this is how to draw a 75-degree angle.

Practice Question MCQs

1. The angle that is less than 360° but more than 180° is referred to as ________.

  1. Reflex Angle

  2. Acute Angle

  3. Right Angle

  4. Obtuse Angle

Answer: A) Reflex Angle


2. What do we call an angle that is exactly equal to 180°?

  1. ObtuseAngle

  2. Right Angle

  3. Straight Angle

  4. Acute Angle

Answer: C) Straight Angle


Conclusion

A geometric shape generated by the intersection of two line segments, lines, or rays is known as an angle. Angles, as opposed to linear distance, are a measure of rotational distance. An angle can alternatively be considered as a part of a circle. The angle between two line segments is the distance (in degrees or radians) that one segment must be turned about the crossing point in order for the two segments to overlap. Angles are essential in the definition and study of polygons such as triangles and quadrilaterals. They are utilized in a number of fields, including animation, woodworking, and physics.

FAQs on Constructing Angles

1. How to Construct a 60 degree Angle?

Here we are explaining how to make a 60-degree angle with a compass and we have added the steps of construction of a 60-degree angle for your convenience:

  • Step 1: Draw a ray and name it OA.

  • Step 2: Take O as a centre and any radius of your choice. Draw an arc at the top of OA cutting it at a point B.

  • Step 3: Let B be the centre and with the same radius, draw another arc to fragment the previous arc at point C.

  • Step 4: Join OC and produce it to D.

  • Step 5: Here you have your desired angle ∠AOD = 60 degrees.

2. How to Construct the 120-degree angle?

Here we are explaining how to make a 120-degree angle with a compass and we have added the steps of construction of a 120-degree angle for your convenience:

  • Step 1: Draw a ray OA.

  • Step 2: Let O be the centre and take any radius, draw an arc cutting OA at B.

  • Step 3: Take B as the centre and the same radius cut the arc at C, then with C as the centre and the same radius cut the arc at D. Join OD and stretch it to E.

  • Step 4: Here you have your desired angle ∠AOE=120 degrees.

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