# CONSTRUCTION OF ANGLES USING RULER AND COMPASS

In this section, you will learn how to construct angles using ruler and compass.

To construct an angle, we must need the following mathematical instruments.

1. Ruler

2. Compass

## Examples

Example 1 :

Construct an acute angle of 60°.

Step 1 :

Draw a line ‘l’ and mark a point ‘O’ on it. Step 2 :

(i) With ‘O’ as center draw an arc of any radius to cut the line at A.

(ii) With the same radius and A as center draw an arc to cut the previous arc at B. Step 3 :

(i) Join OB.

(ii) We get the required angle AOB = 60°. Example 2 :

Construct an acute angle of 30°.

Step 1 :

(i) First let us construct 60° angle and then bisect it to get 30° angle.

(ii) Construct 60° (as shown in the above example). Step 2 :

(i) With ‘A’ as center, draw an arc of radius more than half of AB in the interior of AOB.

(ii) With the same radius and with B as center draw an arc to cut the previous one at C.

(iii) Join OC.

(iv) We get the required angle AOC  =  30°. Example 3 :

Construct an obtuse angle of 120°.

Step 1 :

Draw a line ‘l’ and mark a point ‘O’ on it. Step 2 :

With ‘O’ as center draw an arc of any radius to cut the line l at A. Step 3 :

(i)  With same radius and with ‘A’ as center draw another arc to cut the previous arc at ‘B’.

(ii)  With ‘B’ as center draw another arc of same radius to cut the first arc at ‘C’. Step 4 :

(i)  Join OC.

(ii)  We get the required angle AOC  =  120°. Example 4 :

Construct a right angle  90°.

Step 1 :

(i)  To construct 90° angle, we are going to bisect the straight angle 180°.

(ii)  Mark a point ‘O’ on a straight line ‘l’. Step 2 :

(i)  With ‘O’ as center draw arcs of any radius to cut the line l at A and B.

(ii)  Now AOB  =  180°. Step 3 :

With A and B as centers and with the radius more than half of AB draw arcs above AB to intersect each other at ‘C’. Step 4 :

(i)  Join OC.

(ii)  We get the required angle AOC  =  90°.  Apart from using ruler and compass, we can construct angles using ruler and protractor also.

To know how to construct angles using ruler and protractor,

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