Question

In the given figure ‘O’ is the centre of the circle. If QR = OP and ∠ORP = 20°. Find the value of ‘x’ giving reasons.

Answer 1

Given:

ΔRQP me RQ = OQ

Therefore ∠QRO = ∠RQR = 20°

Using the sum of angles:

∠RQP = 180° − 20° − 20° = 140°

Linear pair:

∠RQP + ∠OQP = 180°

∠OQP = 40°

In ΔOPQ, OP = OQ (radii)

∠OPQ = ∠OQP = 40°

Sum of angles:

∠POQ = 100°

Straight line:

x + 100° + 20° = 180°

x = 60°