Question

In the adjoining figure DE || QR. AP and BP are bisectors of AngleEAB and angleRBA respectively. Find angleAPB

Answer 1

it is way while first,

as it is transversal

angle EAB + angle ABR =180

as AP and BP are bisectors

angle 1/2(PAB) = x and

angle 1/2(PBA )=y

therefore x+x+y+y=180

2x+2y=180

2(x+y)=180

x+y=90...(1)

therefore now

x+y+APB=180

and from eq. 1

APB = 90