#### 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.

#### 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°