Answer:
x = 50 and y = 10
Step-by-step explanation:
The drawing shows several equal sides. The triangles are a reflection of each other, so their angles will be the same.
Take the top and bottom angles:
2x + 5 and 3x - 45
They are equal, so:
2x + 5 = 3x - 45
-x = -50
x = 50
The angle y will have the same value as the one below it in the bottom triangle. Add the angles in the lower triangle and since the sum of the angles in a triangle is always 180, we can say:
y + (8y-15) + (3x-45) = 180
Rearrange:
y = 180 - (8y-15) - (3x-45)
y = 180 - 8y + 15 - 3x + 45
9y = 180 + 15 - 3x + 45
Since x = 50:
9y = 180 + 15 - 3*(50) + 45
9y = 180 + 15 - 150 + 45
9y = 90
y = 10
