in a parallelogram abcd , the bisectors of the consecutive angles angle A AND angle b intersect at p , show that apb is 90

in a parallelogram abcd , the bisectors of the consecutive angles angl

1.	in a parallelogram abcd , the bisectors of the consecutive angles angle A AND angle b intersect at p , show that apb is 90
Answer» -➦ A parallelogram ABCD➦ AP AND BP are bisectors of consecutive ANGLES ∠A and ∠B which INTERSECT at PRTP :-➦ ∠APB = 90°Solution :-➦ We know, sum of the consecutive angles of a parallelogram will be SUPPLEMENTARY (180°)➦ ∠A + ∠B = 180°➦ ½∠A + ½∠B = ¹⁸⁰⁄₂➦ ∠PAB + ∠APB = 90°➦ In ΔAPB :-➦ ∠PAB + ∠APB + ∠PBA = 180° (Angle sum property)➦ ∠APB = 180° - (∠APB + ∠PBA)➦ 180° - 90°➦ 90°Hence, we proved ∠APB = 90°