QQuestion
In the given diagram, PS and PT are tangents to the circle. SQ ∥ PT and ∠SPT = 80°. The value of ∠QST is:
(a) 140°
(b) 90°
(c) 80°
(d) 50°
✓Answer
(d) 50°
Explanation:
PS = PT because tangents drawn from the same external point are equal.
Therefore, △PST is isosceles.
Let ∠PST = ∠PTS = a.
Using the angle-sum property of △PST:
a + a + 80° = 180°
⇒ 2a = 100°
⇒ a = 50°
Since SQ ∥ PT, ∠QST = ∠STP by alternate interior angles.
Therefore, ∠QST = 50°.
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