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In figure, if PQ || RS, ∠MXQ = 135° and ∠MYR = 40° then find ∠XMY.

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ago by (27.5k points)
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Best answer

Construction: Draw a line || to PQ or RS through M

TZ || PQ

⇒ 135° + ∠1 = 180°

⇒ ∠1 = 180° – 135° = 45° …(i)

(Sum of interior angles on the same side of a transversal is 180°)

Also RS || TZ …(ii)

⇒ ∠2 = 40° (alternate interior angle)

Adding (i) and (ii), we get

∠1 + ∠2 = 45° + 40°

= 85°

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