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Question

# In the adjoining figure line p ∥ line q. Line t and line s are transversals. Find measure of ∠x and ∠y using the measures of angles given in the figure.

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Solution

## Let us mark the points P and Q on p; R and S on q; A and B on t; C and D on s. Suppose PQ and AB intersect at K; PQ and CD intersect at X. Suppose RS and AB intersect at L; RS and CD intersect at Y. Since, AB is a straight line and ray KQ stands on it, m∠AKX + m∠XKL = 180° (angles in linear pair) ⇒ 40° + m∠XKL = 180° ⇒ m∠XKL = 180° − 40° ⇒ m∠XKL = 140° Since, p||q and t is a transversal, then m∠YLB = m∠XKL (Corresponding angles) ⇒ x = 140° Since, RS and CD are two straight lines intersecting at Y, then m∠XYL = m∠SYD (Vertically opposite angles) ⇒ m∠XYL = 70° Since, p||q and s is a transversal, then m∠KXY + m∠XYL = 180° (Interior angles on same side of transversal are supplementary) ⇒ y + 70° = 180° ⇒ y = 180° − 70° ⇒ y = 110°

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