Answer is X= 16 Y= 17
Step by step
The lower straight angle LRN gives us angles 7x, x and 52 that added together equals 180 degrees
So our equation is
7x + x + 52 = 180
Combine like terms
8x + 52 = 180
Subtract 52 from both sides to isolate x
8x + 52 - 52 = 180 - 52
8x = 128
Divide both sides by 8 to solve
x = 16
Now we can solve for y
Straight angle MRP gives us 7x and 4y, which will equal 180 degrees. Our equation is
7x + 4y = 180
We know x = 16
7(16) + 4y = 180
112 + 4y = 180
Subtract 112 from both sides to isolate y
112 - 112 + 4y = 180 - 112
4y = 68
Divide both sides by 4 to solve
4/4 y = 68/4
y = 17