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in Angles and Pairs of Angles by (47.6k points)
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Lines PQ and RS intersect at point M. m∠PMR = x°.What are the measures of ∠PMS, ∠SMQ and ∠QMR?

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∠PMR and ∠PMS are angles in a linear pair. 

∴ m∠PMR + m∠PMS = 180° 

∴ x + m∠PMS = 180 

∴ m∠PMS = (180-x)° 

m∠QMR = m∠PMS = (180 – x)° … . (Vertically opposite angles) 

m∠SMQ = m∠PMR = x° …. (Vertically opposite angles) 

∴The measures of ∠PMS, ∠SMQ and ∠QMR are (180 – x)° , x° and (180 – x)° respectively.

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