Question

Two angles of a triangle have equal measures, but the third angle measure is 36 degrees less then the sum of the other two. Find the measure of each angle of the trianlge

Answer 1

Let each one of the two congruent angles have measure x.
The third angle's measure is x + x - 36
We know that the sum of the measures of the angles of a triangle equals 180 deg.
We add the measures of the three angles, and we set the sum equal to 180.
Then we solve for x.

x + x + x + x - 36 = 180

4x - 36 = 180

4x = 216

x = 54

The two congruent angles measure x, so their measure is 54.
The measure of the third angle is x + x - 36 = 54 + 54 - 36 = 72

The measures of the three angles are 54 deg, 54 deg, 72 deg.