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In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.

Solution:

Given, ABC is a triangle

The measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C.

We have to find the measure of ∠A.

According to the question,

∠A = ∠B - 40°

∠C = ∠B - 40° + 50°

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,

∠A + ∠B + ∠C = 180°

∠B - 40° + ∠B + ∠B - 40° + 50° = 180

3∠B - 80° + 50° = 180°

3∠B - 30° = 180°

3∠B = 180° + 30°

3∠B = 210°

∠B = 210°/3

∠B = 70°

So, ∠A = 70° - 40° = 30°

Therefore, the measure of angle A is 30°.

✦ Try This: In a triangle XYZ, the measure of angle X is 20° less than the measure of angle Y and 60° less than that of angle Z. Find the measure of ∠X.

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 111

In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.

Summary:

In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. The measure of ∠A is 30°.

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