Answer is x= 8 and y= 21
Step by step
Let’s break this down
We know straight angle AB = 180 degrees so the sum of all angles will = 180
We know there is a right angle EOG = 90
Let’s solve the two angles inside this right angle. The sum of EOF = 27 and FOG = 3y will = 90 degrees (right angle)
Our equation is 27 + 3y = 90
Subtract 27 from both sides to isolate y
27 -27 +3y = 90 - 27
Combine
3y = 63
Divide both sides by 3 to solve y
3/3 y = 63/3
y = 21
So now let’s solve for x
Since we know EOG is 90 degrees, we know the other two unknown angles AOE = x and BOG = 8x + 18 sum will equal 90 degrees, because all straight angles sum = 180
So our equation is
x + 8x + 18 = 90
Combine like terms
9x + 18 = 90
Subtract 18 from both sides to isolate x
9x +18 -18 = 90 -18
Combine
9x = 72
Divide both sides by 9 to solve
9/9 x = 72/9
x = 8
Check your work
x + 27 + 3y + 8x + 18 = 180
(8) + 27 + (3)(21) + (8)(8) + 18 = 180
8 + 27 + 63 + 64 + 18 = 180
180 = 180
Problem solved!