#### Question

The given figure shows a circle with centre O and ∠ABP = 42°

Calculate the measure of:

(i) ∠PQB

(ii) ∠QPB + ∠PBQ

#### Solution

Join AP.

(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°

Is there an error in this question or solution?

Solution The Given Figure Shows a Circle with Centre O and ∠Abp = 42°Calculate the Measure Of: (I) ∠Pqb (Ii) ∠Qpb + ∠Pbq Concept: Arc and Chord Properties - Angles in the Same Segment of a Circle Are Equal (Without Proof).