Find x and y. give reasons to justify your solutions.

x=8°, y=21°

Step-by-step explanation:

AOB is a linear angle, hence 180°. It is the sum of angles AOE, EOG, and GOB. Angle EOG is marked as a right angle, so we have ...

... x + 90° + (8x+18°) = 180°

... 9x = 72° . . . . . collect terms, subtract 108°

... x = 72°/9

... x = 8°

We noted above that EOG is a right angle. It is the sum of angles EOF and FOG, so we have

... 27° + 3y = 90°

... 9° + y = 30° . . . . . divide by 3

... y = 30° -9° . . . . . . subtract 9°

... y = 21°

check the picture below.