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

• Given: Line p || line q, line t and line s are transversals.

• To find: The measure of ∠x and ∠y.

Here we can see

∠KLD=∠HLD (∵ Opposite angles are equal)

⇒ ∠ KLD=70°

∠KLI+∠JIL=180° (∵ (∵ Property of interior angles.)

∴ 70+Y=180°

⇒ Y=110°

∴ The value of y is 110°

Also,

∠ BKL+∠ JKL =180° (Linear pair)

⇒ x+∠JKL = 180°

∴ ∠ JKL= 180-x…(1)

∠ KJI+∠ AJI =180° (Linear pair)

⇒ 40+∠KJI = 180°

∴ ∠ KJI= 140°…(2)

Now,

∠KJI+∠JKL=180° (∵ Property of interior angles.)

140+180-x=180 (From 1 and 2)

⇒-x=180-180-140

⇒ -x=-140°

∴ x=140°

∴ The value of x is 140°.