Q110 of 158 Page 159

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.

Given: ∠Z = 90°


∠X is 30° greater than ∠Y


Formula Used/Theory:-


→ Angle sum property


Sum of all angles of triangle is 180°


Let ∠Y be ‘a’


Then;


∠X = ∠Y + 30°


∠X = a + 30°


∠Z = 90°


By angle sum property


∠X + ∠Y + ∠Z = 180°


(a + 30°) + a + 90° = 180°


2a + 120° = 180°


2a = 180° - 120° = 60°


a = = 30°


∠Y = a


∴ ∠Y = 30°


Result:- Measure of ∠Y comes to be 30°


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