M A T and TAH are supplementary angles. The angles have the following measures: M A T = (6x - 6) degrees and TAH = (4x - 14) degrees. What is an equation to solve for x?

Question

A. 9x degrees - 20 degrees = 180 degrees
B. 10x degrees + 20 degrees = 180 degrees
C. 10x degrees - 20 degrees = 180 degrees
D. x degrees - 20 degrees = 180 degrees

Answer 1

B. 10x degrees + 20 degrees = 180 degrees

Since MAT and TAH are supplementary angles, the sum of their measures is 180 degrees. Therefore, the equation to solve for x is:

(6x - 6) + (4x - 14) = 180
10x - 20 = 180
10x = 200
x = 20

Substitute x=20 back into the angle measures to verify. The angle measures are:
MAT = (6(20) - 6) = 114 degrees
TAH = (4(20) - 14) = 66 degrees

114 + 66 = 180, which confirms that x=20 is the correct value.