Find the value of unknown angles in the following figures :

1.	Find the value of unknown angles in the following figures :
Answer» (i) ∵∠x+ 125°= 180° ∠x = 180°- 125° = 55° Two lines intersect each other ∴ ∠y = 125° (vertically opposite angles) (ii) ∠x + 20° = 180° [ ∠x = 180° – 20°= 160°] (iii) Two lines intersect each other ∠x = 55° (vertically opposite angles) ∵ ∠x + ∠z = 180° (x, z is a linear pair whose sum is 180°) 55° + ∠z = 180° ⇒ ∠z = 180°- 55°= 125° Clearly ∠y + ∠x = 90° ∠y + 55° = 90° ∠y = 90° – 55° = 35°

Answer»

(i) ∵∠x+ 125°= 180°

∠x = 180°- 125° = 55°

Two lines intersect each other

∴ ∠y = 125° (vertically opposite angles)

(ii) ∠x + 20° = 180°

[ ∠x = 180° – 20°= 160°]

(iii) Two lines intersect each other

∠x = 55° (vertically opposite angles)

∵ ∠x + ∠z = 180° (x, z is a linear pair whose sum is 180°)

55° + ∠z = 180°

⇒ ∠z = 180°- 55°= 125°

Clearly ∠y + ∠x = 90°

∠y + 55° = 90°

∠y = 90° – 55° = 35°

Discussion