Ex 11.1, 3 - Chapter 11 Class 9 Constructions

Ex 11.1, 3

Construct the angles of the following measurements :

(i) 30°

Steps of Construction :

1. Draw ray OA
2. Taking A as centre and some radius, draw an arc of a circle, which intersects OA at Point B.
3. Taking B as Centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C.
4. Draw the ray AD Passing through C.
   Thus, ∠ AOD = 60°
   Now we draw bisector of ∠ AOD
5. Taking C and D as Centre , with radius more than 1/2CD, draw arcs intersecting at E.
6. Join OE

Thus, ∠ AOE = 30°

(ii) 221/2°

221/2 = 45/2

So, we make 45° and then make its bisector

Steps of construction

1. Draw a ray OA.
2. Taking O as centre and any radius, draw an arc cutting OA at B.
3. Now, taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C.
4. With C as centre and the same radius, draw an arc cutting the arc at D.
5. With C and D as centres and radius more than 1/2 CD draw two arcs intersecting at P.
6. Join OP.  Thus, ∠ AOP = 90°
7. Now, take B and Q as centers, and radius greater than 1/2 BQ, draw two arcs intersecting at R.
8. Join OR. 
   Thus, ∠ AOR = 45
9. Now, take B and S as centers, and radius greater than 1/2 BS, draw two arcs intersecting at T.
10. Join OT. 

Thus, ∠ AOT = 221/2°

(iii) 15°

15°  = 30/2

So, we make bisector of 30°

Steps of Construction :

1. Draw ray OA
2. Taking A as centre and some radius, draw an arc of a circle, which intersects OA at Point B.
3. Taking B as Centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C.
4. Draw the ray AD Passing through C.
   Thus, ∠ AOD = 60°
5. Taking B and C as Centre , with radius more than 1/2 BC, draw arcs intersecting at E.
6. Join OE
   Thus, ∠ AOE = 30°
7. Taking B and P as Centre , with radius more than 1/2BP, draw arcs intersecting at F.
8. Join OF

Thus, ∠ AOF = 15°