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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°

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Transcript

Ex 11.1, 3 Construct the angles of the following measurements : 30° Steps of Construction : Draw ray OA Taking A as centre and some radius, draw an arc of a circle, which intersects OA at Point B. Taking B as Centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C. Draw the ray AD Passing through C. Thus, ∠ AOD = 60° Now we draw bisector of ∠ AOD Taking C and D as Centre , with radius more than 1/2CD, draw arcs intersecting at E. Join OE Thus, ∠ AOE = 30° Ex 11.1, 3 Construct the angles of the following measurements : 221/2° 221/2 = 45/2 So, we make 45° and then make its bisector Steps of construction Draw a ray OA. Taking O as centre and any radius, draw an arc cutting OA at B. Now, taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C. With C as centre and the same radius, draw an arc cutting the arc at D. With C and D as centres and radius more than 1/2 CD draw two arcs intersecting at P. Join OP. Thus, ∠ AOP = 90° Now, take B and Q as centers, and radius greater than 1/2 BQ, draw two arcs intersecting at R. Join OR. Thus, ∠ AOR = 45 Now, take B and S as centers, and radius greater than 1/2 BS, draw two arcs intersecting at T. Join OT. Thus, ∠ AOT = 221/2° Ex 11.1, 3 Construct the angles of the following measurements : 15° 15° = 30/2 So, we make bisector of 30° Steps of Construction : Draw ray OA Taking A as centre and some radius, draw an arc of a circle, which intersects OA at Point B. Taking B as Centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C. Draw the ray AD Passing through C. Thus, ∠ AOD = 60° Taking B and C as Centre , with radius more than 1/2 BC, draw arcs intersecting at E. Join OE Thus, ∠ AOE = 30° Taking B and P as Centre , with radius more than 1/2BP, draw arcs intersecting at F. Join OF Thus, ∠ AOF = 15°

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