Question

In triangle XYZ, the measure of angle X is 30° greater than the measure of angle Y and angle Z is a right angle. Find the measure of ∠Y.

Answer 1

According to the question,

Measure of ∠X = ∠Y + 30°

Measure of ∠Z = 90°

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

i.e. ∠X + ∠Y + ∠Z = 180°

⇒ ∠Y + (∠Y + 30°) + 90° = 180°

⇒ 2∠Y + 120° = 180°

⇒ 2∠Y = 180° – 120° = 60°

∴  ∠Y = `60^circ/2` = 30°