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

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.