If p ॥ q and q ॥ r then find the value of x and y.

1.	If p ॥ q and q ॥ r then find the value of x and y.
Answer» In figure (i) p ॥ q ∴ ∠x = 95° and ∠x + 30° + ∠y= 180° (Linear pair) 95°+ 30 ° + ∠y = 180° 125° + ∠y = 180° ∠y = 180°- 125° = 55° In figure (ii) p ॥ q and q ॥ r ∴ ∠y = 65° (Alternate angles) and ∠x + ∠y = 180° (Linear pair) ∠x + 65° = 180° ∠x = 180° -65°= 115°

Answer»

In figure (i) p ॥ q

∴ ∠x = 95°

and ∠x + 30° + ∠y= 180° (Linear pair)

95°+ 30 ° + ∠y = 180°

125° + ∠y = 180°

∠y = 180°- 125° = 55°

In figure (ii) p ॥ q and q ॥ r

∴ ∠y = 65° (Alternate angles)

and ∠x + ∠y = 180° (Linear pair)

∠x + 65° = 180°

∠x = 180° -65°= 115°

Discussion