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

*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°**.

*Step of Construction:*

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

**(ii)** Draw the bisector OE of ∠AOD.

Then, **∠AOD = 30°**.

*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°**.

*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°**.

*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°**.

*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°**.

*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°**.

**● ****Angle.**

**Interior and Exterior of an Angle.**

**Measuring an Angle by a Protractor.**

**Construction of Angles by using Compass.**

**Geometry Practice Test on angles.**

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