Question

In a convex quadrilateral pqrs, angle spr= 80°, angle qpr= 40°, angle sqr=40° and pr=ps.If diagonals qs and pr intersect at o, then find angle poq

Answer 1

In given convex quadrilateral PQRS Angle POQ = 110°

Step-by-step explanation:

∠SPR = 80°

PR = PS

in Δ PRS

∠PSR = ∠PRS

& ∠SPR + ∠PSR + ∠PRS = 180°

=> ∠PSR = ∠PRS = 50°

As PS = PR

so we can say if P is center then S & R lies on circle

Now ∠SQR = 40° = (1/2) 80° = (1/2) ∠SPR

=> Q will also lie on circle

=> PQ = PR = Radius

=> ∠PRQ = ∠PQR

in Δ PQR

∠QPR + ∠PRQ + ∠PQR = 180°

=> 40° + ∠PRQ + ∠PQR = 180°

=> ∠PRQ = ∠PQR = 70°

∠POQ = ∠OQR + ∠QRO

=> ∠POQ = ∠SQR + ∠QRP

=>  ∠POQ = 40° + 70°

=> ∠POQ = 110°