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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.
Solution
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°
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