Question

In the adjoining figure, PT is a tangent at T to the circle with centre O. If ∠TPO = 30°, find the value of x.

Answer 1

Given:

• PT is a tangent to the circle at point T.

• O is the centre of the circle.

• ∠TPO = 30°.

• We have to find ∠x = ∠PTO.

The radius OT is perpendicular to the tangent PT at the point of contact T.

∴ ∠OTP = 90°

∠OTP = 90°, ∠TPO = 30°, ∠x = ?

The sum of angles in a triangle = 180°

∠OTP + ∠TPO + ∠x = 180°

90° + 30° + x = 180°

x = 180° − 120° = 60°

x = 60°​