Question

Lines PQ and RS intersect at point M. m∠PMR = x^° What are the measures of ∠PMS, ∠SMQ and ∠QMR?

Answer 1

In the given figure,
∠RMP + ∠PMS = 180^∘ (Linear Pair angles)
⇒ x^∘ + ∠PMS = 180^∘
⇒ ∠PMS = (180 − x)^∘
Now,
∠PMR = ∠SMQ = x^∘ (Vertically opposite angles)
∠PMS = ∠RMQ = (180 − x)^∘ (Vertically opposite angles)
Hence, the measures of ∠PMS, ∠SMQ and ∠QMR are (180 − x)^∘, x^∘ and (180 − x)^∘ respectively.