The third angle in an isosceles triangle is half as large as each of the two base angles. Find the measure of each angle

Answer 1

An isosceles triangle has two equal sides and two equal angles opposite those sides, called base angles.

Let these two base angles have measure x°. It's given that the third angle is half as large, so the measure of the third angle is x°/2.

The angle measures in a triangle add to 180°, so set the sum of x, x, and x/2 to 180 to solve for x.

x + x + x/2 = 180

2x/2 + 2x/2 + x/2 = 180

5x/2 = 180

5x = 360

x = 72

The value of x is 72, so the two base angles (x°) are 72°, and the third angle (x°/2) is 36°.