Two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two. Find the measure of each angle of the triangle.

Draw a triangle and label is ABC.

Let angle A = x

let angle B = x

let angle C = 2x - 36

2x - 36 means that angle C is 36 degrees less than the sum of angle A and B.

Since the sum of the interior angles of a triangle is 180 degrees, then 2x + 2x - 36 = 180.

combine like terms in that equation and you get 4x - 36 = 180

add 36 to both sides of that equation and you get 4x = 216

divide both sides of that equation by 4 and you get x = 54 degrees

angle A = 54 degrees

angle B = 54 degrees

angle C = 108 - 36 = 72 degrees

54 + 54 + 72 = 108 + 72 = 180 degrees so the angles are good because they add up to 180 degrees and the third angle is 36 degrees less than the sum of the other 2.