Question

in a parallelogram ABCD the bisectors of consecutive angles A and B interest at B show that angle APB = 90°

Answer 1

Sum of Alternate angles of llgm are supplementary (180° sum)

So as AP and BP are angle bisector

A+B=180°

1/2(A+B)=90°. (1)

By Angle sum property of triangle we have

1/2A +1/2B +APB =180°

As by equation (1) we have

APB =180°-90°=90°

Hence proved