Answer:
y = 3 or y = 5
x = 171 or 155
Step-by-step explanation:
This question uses the alternate interior angles theorem (alternate interior angles are equal) and the same side interior angles theorem (same side interior angles are supplementary). Using this, we can find our answers:
Create equation
y^2 = 8y - 15
Subtract 8y - 15 from both sides
y^2 - 8y + 15 = 0
Factor
(y - 3)(y - 5) = 0
Set factors equal to 0
y - 3 = 0
y - 5 = 0
Add 3 or 5 to both sides
y = 3 or y = 5
We can now figure out x as well:
Create equation
x + y^2 = 180
Fill in y
x + 9 = 180
x + 25 = 180
Subtract 9 or 25 from both sides
x = 171 or x = 155
Hope this helps!
