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.