Answer:
Explanation:
Because of the Isosceles Triangle Theorem, both the base angles of that triangle measure a. We also know that a + b = 180 because of the definition of supplementary angles. So we have 2 equations from that info. First is the fact that
a + 7x = 180 and the second is
2x + a + a = 180 because of the Triangle Angle-Sum Theorem. If the left side of the first equation = 180 and the left side of the second equation also = 180, then by the transitive property of equality,
a + 7x = 2x + a + a and
a + 7x = 2x + 2a and
5x = a. Now that we know that a = 5x, we go back to our triangle and fill in 5x as a:
5x + 5x + 2x = 180 (the Triangle Angle-sum Theorem again) and
12x = 180 so
x = 15. If x = 15, then
a = 5(15) = 75,
b = 7(15) = 105, and
c = 2(15) = 30