Question

In the adjoining figure AB is diameter of circle with centre O then find angle PBA and BAR

Answer 1

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Hey Mate!!

∠ARB = 90°        (∵Angle in a semi-circle)

In ΔARB,

∠ARB + ∠RBA + ∠BAR = 180°    (∵Angle Sum Property)

⇒ 90° + 50° + ∠BAR = 180°

⇒ 130° + ∠BAR = 180°

⇒ ∠BAR = 180° - 130°

→ ∠BAR = 50°

∠APB = 90°        (∵Angle in a semi-circle)

In ΔAPB,

∠APB + ∠PBA + ∠BAP = 180°    (∵Angle Sum Property)

⇒ 90° + 55° + ∠PBA = 180°

⇒ 135° + ∠PBA = 180°

⇒ ∠PBA = 180° - 135°

→ ∠PBA = 45°