Question

In the following figure, find the measures of ∠x and ∠y.

Answer 1

In ∆ABC,

∠BAC + ∠ABC + ∠ACB = 180°  ...[Angle sum property]

⇒ 45° + 60° + x = 180°

⇒ x = 180° – 45° – 60° = 75° ...(i)

Now, ∠BAD = ∠ABC + ∠ACB  ...[Exterior angle property]

⇒ y = 60° + x

⇒ y = 60° + 75° = 135°  ...[Using (i)]

Thus, x = 75° and y = 135°