Question

in the given figure line pq and line rs intersect at point o prove that angle pos = angle roq ​

Answer 1

PQ and RS are two lines intersecting at O as shown in Fig. They lead to two pairs of vertically opposite angles, namely,

(i) ∠POS and ∠ROQ (ii) ∠POR and ∠SOQ.

We need to prove that ∠POS = ∠ROQ and ∠POR = ∠SOQ. ∠AOC = ∠BOD and ∠AOD = ∠BOC.

Now, ray OP stands on line RS.

Therefore, ∠POS + ∠POR = 180° (Linear pair axiom) …..(1)

Can we write ∠POR + ∠ROQ = 180°? (Linear pair axiom ……(2)

From (1) and (2), we can write

∠POS + ∠POR = ∠POR + ∠ROQ

This implies that ∠POS = ∠ROQ

Similarly, it can be proved that ∠POS = ∠ROQ

and also, ∠POR = ∠SOQ