Question

Find the value of x, y and z in each of the following :

Answer 1

(i) Two lines intersects each other

∴ ∠x = ∠55°, (Vertically opposite angles)

∴ x + z = 180° (Linear pair angle)

⇒ 55° + ∠z = 180°

⇒ ∠z = 180°- 55° = 125°

Clearly ∠z = ∠y, (Vertically opposite angles)

⇒ ∠y = 125°

∠x = 55°, ∠y = 125°

and ∠z = 125°.

(ii) 40° + ∠x + 25° = 180° (Straight angle)

⇒ 65 + ∠x = 180°

⇒ ∠x = 180° – 65° = 115°

and ∠y + 40° = 180°, (Linear pair angle)

⇒ ∠y= 180° – 40° = 140°

and ∠y + ∠z = = 180°, (Linear pair angle)

∠z = 180°- ∠y

= 180°- 140° = 40°

∴ ∠x = 115°, ∠y = 140° and ∠z = 40°