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