Mathematics
In the figure (i) given below, O is the center of the circle and ∠PBA = 42°. Calculate the value of ∠PQB.
Circles
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Answer
Considering △APB,
∠APB = 90° (∵ angle in a semicircle is 90°.)
We know that sum of angles of triangle is 180°.
⇒ ∠APB + ∠PBA + ∠PAB = 180°.
⇒ 90° + 42° + ∠PAB = 180°
⇒ 132° + ∠PAB = 180°
⇒ ∠PAB = 180° - 132°
⇒ ∠PAB = 48°.
Considering △PAB and △PQB,
∠PAB = ∠PQB = 48° (∵ angles in same segment are equal.)
Hence, the value of ∠PQB = 48°.
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