# Construction of Angles by using Compass

In construction of angles by using compass we will learn how to construct different angles with the help of ruler and compass.

### 1. Construction of an Angle of 60° by using Compass

Step of Construction:

(i) Draw a ray OA.

(ii) With O as centre and any suitable radius draw an arc above OA cutting it at a point B.

(iii) With B as centre and the same radius as before, draw another arc to cut the previous arc at C.

(iv) Join OC and produce it to D. Then ∠AOD = 60°.

### 2. Construction of an Angle of 120° by using Compass

Step of Construction:

(i) Draw a ray OA.

(ii) With O as centre and any suitable radius draw an arc cutting OA at B.

(iii) With B as centre and the same radius cut the arc at C, then with C as centre and same radius cut the arc at D. Join OD and produce it to E. Then, ∠AOE = 120°.

### 3. Construction of an Angle of 30° by using Compass

Step of Construction:

(i) Construction an angle ∠AOD = 60° as shown.

(ii) Draw the bisector OE of ∠AOD. Then, ∠AOD = 30°.

### 4. Construction of an Angle of 90° by using Compass

Step of Construction:

(i) Take any ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at B.

(iii) With B as centre and the same radius, draw an cutting the first arc at C.

(iv) With C as centre and the same radius, cut off an arc cutting again the first arc at D.

(v) With C and D as centre and radius of more than half of CD, draw two arcs cutting each other at E, join OE. Then, ∠EOA = 90°.

### 5. Construction of an Angle of 75° by using Compass

Step of Construction:

(i) Take a ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at C.

(iii) With C as centre and the same radius, draw an cutting the first arc at M.

(iv) With M as centre and the same radius, cut off an arc cutting again the first arc at L.

(v) With L and M as centre and radius of more than half of LM, draw two arcs cutting each other at B, join OB which is making 90°.

(vi) Now with N and M as centres again draw two arcs cutting each other at P.

(vii) Join OP. Then, ∠POA = 75°.

### 6. Construction of an Angle of 105° by using Compass

Step of Construction:

(i) After making 90° angle take L and N as centre and draw two arcs cutting each other at S.

(ii) Join SO. Then, ∠SOA = 105°.

### 7. Construction of an Angle of 135° by using Compass

Step of Construction:

(i) Construct ∠AOD = 90°

(ii) Produce ∠AO to B.

(iii) Draw OE to bisect ∠DOB.

∠DOE = 45°

∠EOA = 45° + 90° = 135° Then, ∠EOA = 135°.

### 8. Construction of an Angle of 150° by using Compass

Step of Construction:

(i) Construct ∠AOC = 120°

(ii) Produce ∠AO to B.

(iii) Draw OD to bisect ∠COB.

Now ∠COD = 30°

Therefore, ∠AOD = 120° + 30° = 150° Then, ∠AOD = 150°.

Interior and Exterior of an Angle.

Measuring an Angle by a Protractor.

Types of Angles.

Pairs of Angles.

Bisecting an angle.

Construction of Angles by using Compass.

Worksheet on Angles.

Geometry Practice Test on angles.