Each of the two equal angles of an isosceles triangle is four times the third angle. Find the angles of the triangle.

Solution:

Given, each of the two equal angles of an isosceles triangle is four times the third angle.

We have to find the angles of the triangle.

Consider an isosceles triangle ABC,

An isosceles triangle is a triangle that has two sides of equal length.

The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.

AB = AC

In an isosceles triangle, the side opposite the vertex angle is called the base and base angles are equal.

So, ∠B = ∠C

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

According to the question,

Let the third angle be x

So, two equal angles are 4x and 4x.

By angle sum property,

∠A + ∠B + ∠C = 180°

x + 4x + 4x = 180°

9x = 180°

x = 180°/9

x = 20°

So, 4x = 4(20°) = 80°

Therefore, the measure of the angles are 80°, 80° and 20°.

✦ Try This: Each of the two equal angles of an isosceles triangle is two times the third angle. Find the angles of the triangle.

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

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NCERT Exemplar Class 7 Maths Chapter 6 Problem 121

Each of the two equal angles of an isosceles triangle is four times the third angle. Find the angles of the triangle.

Summary:

Each of the two equal angles of an isosceles triangle is four times the third angle. The angles of the triangle are 80°, 80° and 20°.

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☛ Related Questions:

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