Answers: x = 36 degrees, y = 22 degrees.
You can easily find x because of complementary angles, since it is clearly marked as a right angle and all right angles are 90 degrees, you subtract 54 from 90 to find the value of x (90 - 54 = 36). Then, in order to find the value of y, you would need to find the degrees of angle AOC and BOD. Due to supplementary angles, angle AOC and COB should equal 180 degrees when combined. So you subtract 156 from 180 to get you the value of angle AOC (180 - 156 = 24). Since angles AOC and BOD are vertical angles, they are congruent with the same measure of 24 degrees. Now that the only angles left have the y value in them, you combine 2y and y (2y + y = 3y). We know that all of these angles in the diagram combined should be equal to 360, so you add up the angles you already know or have found and subtract that sum from 360 (AOC - 24 degrees, COB - 156 degrees, BOD - 24 degrees, GOF - 36 degrees, FOE - 54 degrees, all combined should = 294 degrees, 360 - 294 = 66). Since you have 66 degrees left to make the diagram true, you divide that by 3 because that’s how many y’s you have (66/3 = 22). And that’s how you get y = 22 degrees.
