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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:

Given, XYZ is a triangle.

The measure of angle X is 30° greater than the measure of angle Y.

Angle Z is a right angle.

We have to find the measure of angle Y.

According to the question,

∠Z = 90°

∠X = ∠Y + 30°

Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.

By angle sum property,

∠X + ∠Y + ∠Z = 180°

∠Y + 30° + ∠Y + 90° = 180°

2∠Y + 120° = 180°

2∠Y = 180° - 120°

2∠Y = 60°

∠Y = 60°/2

∠Y = 30°

Therefore, the value of Y is 30°.

✦ Try This: In triangle ACD, the measure of angle A is 10° greater than the measure of angle C and angle D is a right angle. Find the measure of ∠C.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 110

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.

Summary:

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

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