Please answer the

Please answer the points on circle, A B is a ot the circle. • 'Ibe lines RB intersect Q. Find ZPRB. ZPBR, o 13 Scoring indicators - 340 qScote1

Given, ∠A = 34°, ∠Q = 28°

Now, ∠PAB = ∠PRB = 34° [Angles in the same segment of a circle are equal]

Also, ∠APB = 90°  [Angle in a semi-circle is always a right angle]

⇒ ∠APB + ∠BPQ = 180° [Linear pair]

⇒ ∠BPQ = 180° - 90° = 90°

Now, in triangle PQR, by angle sum property of triangle, we have

∠PQR + ∠RPQ + ∠PRQ = 180°

⇒ ∠RPQ = 180° - 34° - 28° = 118°

Therefore, ∠BPR = ∠RPQ - ∠BPQ = 118° - 90° = 28°

Again, in triangle PBR by angle sum property of triangle, we have

∠PBR + ∠R + ∠BPR = 180°

⇒ ∠PBR = 180° - (∠R + ∠BPR)

= 180° - 34° - 28°

= 118°