In the given diagram, ABC is a straight line.(i) If x = 53°, find y.(

1.	In the given diagram, ABC is a straight line.(i) If x = 53°, find y.(ii) If y =1 1/2 right angles ; find x.
Answer» (i) From the figure, ∠ABD + ∠DBC = 180° (Linear pair of angles) ⇒ x + y = 180° ⇒ 53°+ y = 180° (∵ x = 53”) ⇒ y = 180° – 53° ⇒ y = 127° (ii) From figure again, x + y = 180° 1 + 3/2 x 90 = 180° ⇒ x + 1 1/2 right angles = 180° ⇒ x + 3/2 x 90 =180° ⇒ x + 135°= 180° ⇒ x = 180° – 135° ⇒ x = 45°

In the given diagram, ABC is a straight line.(i) If x = 53°, find y.(ii) If y =1 1/2 right angles ; find x.

Answer»

(i) From the figure,

∠ABD + ∠DBC = 180° (Linear pair of angles)

⇒ x + y = 180°

⇒ 53°+ y = 180° (∵ x = 53”)

⇒ y = 180° – 53°

⇒ y = 127°

(ii) From figure again,

x + y = 180°

1 + 3/2 x 90 = 180°

⇒ x + 1 1/2 right angles = 180°

⇒ x + 3/2 x 90 =180°

⇒ x + 135°= 180°

⇒ x = 180° – 135°

⇒ x = 45°