find the measure of X and Y

Question

Answer 1

The sum of he measures of the interior angles of a polygon is (n-2) * 180, where n is the number of sides.

So the sum of the interior angles of this 6-sided figure is 4 * 180 = 720.

we are given that four of the angles are 90 (right angle, 99, 171 and 159, so the remaining two equal angles are 720 - 90 - 99 - 171 - 159 = 201. The two equal angles (x and y) must both be 201/2 = 101.5.