Answer:
x = 59, y = 59, z = 62
Step-by-step explanation:
This is an isosceles triangle, therefore, the angles that are across from the congruent sides are also congruent: x = y
We also know that by the Triangle Angle Sum Theorem, that all the angles of the triangle add up to equal 180 degrees.
Therefore, x + y + z = 180 and, subbing in our expressions gives us
2x + 31 + 2x + 31 + 5x - 8 = 180 and
9x + 54 = 180 so
9x = 126 and
x = 14
That means that x and y have measures of
2(14) + 31 = 59
If those are 59 each, then
z = 180 - 59 - 59 so
z = 62
Let's check and make sure that sum is in fact 180:
59 + 59 + 62 = 180
