Question

Two angles , angle ABC and angle PQR intersect each other at O such that PQ||AB and QR||BC as shown in the figure: If angle PQR =50° find angle POC and angle ABC.​

Answer 1

Answer:

In ΔABCandΔPQR, AB = PQ, BC = QR; CB and RQ are extended to X and Y respectively. ∠ABX=∠PQY. Prove that ΔABC=ΔPQR.

In ΔABC and ΔPQR

AB=PQ

And BC=QR

CB And RQ extended to X and Y

∠ABX=∠PQY

∠ABC=180

o

−∠ABX=180

o

∠PQY

∠PQR=180

o

−∠PQY=∠ABC

We get in both triangles

AB=PQ

BC=QR

And ∠ABC=∠PQR

Then both triangle are congruent

i.e. ΔABC=ΔPQR

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