Question

One of the exterior angles of an isosceles triangle is 115°. Find the angles of this triangle.

Answer 1

Answer:

Case 1: The measure of interior angles are : 65°, 57.5°, 57.5°

Case 2: The measure of interior angles are : 65°, 65°, 50°

Explanation:

We are given an isosceles triangle. In the triangle two sides and two angles having the same measures.

We are given an exterior angle 115°.

So the corresponding interior angle is 180-115 = 65 degrees.

We need to find other two interior angles.

Case 1:

If the given exterior angle is top of the vertex angle, then the base of the interior angles are:

(180-65) ÷ 2 = 57.5°. {because in isosceles triangle two sides and two angles having the same measures]

So, each base angles measures 57.5°.

The measure of interior angles are : 65°, 57.5°, 57.5°

Case 2:

If the given measure of exterior angle is in base, then one angle must be 65°.

Other angle = (180 - (65 +65)) = 180 - 130 = 50°

The measure of interior angles are : 65°, 65°, 50°

Answer 2

If one of the outer corners of an isosceles triangle is 115 degrees, then the internal angle is 180-115 = 65 degrees.

The task has 2 solutions.

Let the angle at the vertex is 65 degrees. Then the angles at the base are (180-65): 2 = 57.5 degrees.

Let the angle at the base be 65 degrees, then another angle at the base is 60 degrees. The vertex angle is 180- (65 + 65) = 50 degrees.