The given figure shows a circle with centre O and ∠ABP = 42°
Calculate the measure of:
(i) ∠PQB
(ii) ∠QPB + ∠PBQ
Calculate the measure of:
(i) ∠PQB
(ii) ∠QPB + ∠PBQ
Exercise 17 (A) | Q 56 | Page 262
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(i) ∠APB = 90°
(Angle in a semicircle)
∴ ∠BAP = 90° - ∠ABP = 90° - 42° = 48°
Now, ∠PQB = ∠BAP = 48°
(Angle in the same segment)
(ii) By angle sum property of ∆BPQ,
∠QPB + ∠PBQ = 180° - ∠PQB = 180° - 48° = 132°
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