Two angles in a triangle are equal and their sum is four times as the third angle in the triangle. What are the measures of each of the three interior angles?

Question

Quizplus · Accepted Answer

Let x be the measure of the third angle, then the other two angles are also x. We know that the sum of all three angles in a triangle is 180 degrees, so:

x + x + x = 180
3x = 180
x = 60

Therefore, each of the two equal angles is 60 degrees, and the third angle is 4 times that, which is 240 degrees. So the measures of the three angles are 60 degrees, 60 degrees, and 240 degrees.

Two Angles in a Triangle Are Equal and Their Sum