Question

In the given figure, PT and QT are tangents to a circle such that ∠TPS = 45° and ∠TQS = 30°. Then, the value of x is:

Options

• 30°

• 45°

• 75°

• 105°

Answer 1

105°

Explanation:

By the alternate-segment theorem, the angle between a tangent and a chord equals the angle in the opposite arc.

So, ∠TPS = ∠PQS = 45° and ∠TQS = ∠QPS = 30°.

In triangle PQS the angles sum to 180°.

So, x = 180° – 45° – 30° = 105°.