Question

In the given diagram, PS and PT are the tangents to the circle. SQ || PT and ∠SPT = 80°. The value of ∠QST is ______.

Options

• 140°

• 90°

• 80°

• 50°

Answer 1

In the given diagram, PS and PT are the tangents to the circle. SQ || PT and ∠SPT = 80°. The value of ∠QST is 50°.

Explanation:

PS and PT are tangents from an exterior point to a circle from point P

i.e., PS = PT

So ∠PST = ∠PTS

In ΔPST,

∠PST + ∠PTS + ∠SPT = 180°

2∠PTS = 180° – 80° = 100°

∠PTS = 50°

Here, SQ || PT and ST is a transversal

Then, ∠QST = ∠STP = 50° ...(Alternate pair of angles)