Q2 of 12 Page 114

In the figure, arc AXB is a semicircle. m∠PAB = 40°. Hence, find the values of

(1) m∠APB,


(2) m(arc PYB),


(3) m(arc AZP),


As we know that


Inscribed angle of arc is half the angle intercepted by arc


1. ⇒ ∠ APB = *∠ AOB


∠ APB = *180°


∠ APB = 90°


2. ⇒ m(arc PYB) = ∠ POB


∠ POB = 2*∠ PAB


∠ POB = 2*40° = 80°


∴ m(arc PYB) = 80°


3. In Δ APB


∠ A + ∠ P + ∠ B = 180°


∠ B = 180°-∠ P-∠ A


∠ B = 180°-90°-40°


∠ B = 50°


⇒ m(arc AZP) = ∠ POA


∠ POA = 2*∠ PBA


∠ POA = 2*50°


∴ m(arc AZP) = 100°


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