Question

In the following figure, find the values of x, y and z.

Answer 1

In the give figure,

∠BAD = 60°, ∠ABD = 60°, ∠ADB = x, ∠DAC = 30°, ∠ADC = y and ∠ACD = z

We know that, the sum of all angles in a triangle is equal to 180°.

In ΔABD,

∠BAD + ∠ABD + ∠ADB = 180°

⇒ 60° + 60° + x = 180°

⇒ 120° + x = 180°

⇒ x = 180° – 120°

⇒ x = 60°

Now, y = ∠BAD + ∠ABD  ...[∵ Exterior angle is equal to the sum of interior opposite angles]

⇒ y = 60° + 60°

∴ y = 120°

In ΔADC,

∠DAC + ∠ADC + ∠ACD = 180°  ...[Angle sum property of a triangle]

⇒ 30° + 120° + z = 180°

⇒ 150° + z = 180°

⇒ z = 180° – 150°

⇒ z = 30°

Hence, x = 60°, y = 120° and z = 30°.