Question

In the adjacent figure,the bisector of angle A and angle B meet in a point, if angle C=100° and and angle D=60°.find the measure angle APB.​

Answer 1

Hey Bestie!

$\tt\red{∠A+∠B+∠C+∠D=360°}$–––Sum of all the angles of a quadrilateral are 360°

${⇒}$$\tt\pink{∠A+∠B+100°+60°=360°}$

${⇒}$$\tt\purple{∠A+∠B=360°-160}$

${⇒}$$\tt\orange{∠A+∠B=200°}$

${⇒}$$\tt\green{\frac{1}{2}∠A+\frac{1}{2}∠B=100°}$–––AP and PB are the bisectors of ∠BAD and ∠ABC.

${⇒}$$\tt\red{∠PAB+∠PBA=100°}$–––(1)

In ΔAPB,

${⇒}$$\tt\pink{∠PAB+∠PBA+∠APB=180°}$

${⇒}$$\tt\purple{100°+∠APB=180°}$–––from (1)

${⇒}$$\tt\orange{∠APB=180°-100°=80°}$

${↪}$.°. The measure of ∠APB is 80°