# Construction Of Angles

Let us construct angles of different sizes - 60º, 120º, 30º and 90º

1) 60º Angle

The angles in an Equilateral triangle are all 60º in size.

Step 1:  Draw the line PQ.
Step 2:  Hold the compass at point P and draw an arc that passes through Q.
Step 3:  Similarly, place the point of the compass at Q and draw an arc that passes through P

Let this arc cut the arc drawn in Step 2 at R.

Step 4:  Join P to R. The angle QPR is 60º as the triangle PQR is an equilateral triangle.

2) 30º Angle

Let us first construct a equilateral triangle which has 60º angle and bisect it to form an angle of 30º

Step 1:  Draw the arm PQ.
Step 2:  Place the point of the compass at P and draw an arc that passes through Q.
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.
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 T to P. The angle QPT is 30º.

3) 120º Angle

Since 60 º + 120 º = 180 º, 120º is the supplement of 60º.

Therefore let us construct a 60º angle and then extend one of its arms  to construct a 120 º.

4) 90º Angle

To construct a 90º angle we can construct by bisecting a straight angle .

Following steps are used as an alternate method

Step 1:  Draw the arm PA.
Step 2:  Place the point of the compass at P and draw an arc that cuts the arm at Q.
Step 3:  Place the point of the compass at Q and draw an arc of radius PQ that cuts the arc drawn in Step 2 at R.
Step 4:  With the point of the compass at R, draw an arc of radius PQ to cut the arc drawn in Step 2 at S.
Step 5:  With the point of the compass still at R, draw another arc of radius PQ near T as shown.
Step 6:  With the point of the compass at S, draw an arc of radius PQ to cut the arc drawn in step 5 at T.
Step 7:  Join T  to P. The angle APT is 90º.