Question

<MAT and <TAH are supplementary angles have the following measures. <MAT = ( 6x - 6 ) and <TAH = ( 4x - 14 ). What is an equation to solve for x?

10x + 20 = 180

10x - 20 = 180

9x - 20 = 180

x - 20 = 180

Answer 1

To solve for \( x \), we start with the fact that angles \( <MAT \) and \( <TAH \) are supplementary. This means that the sum of their measures is equal to 180 degrees:

\[
<MAT + <TAH = 180
\]

Substituting the expressions for the angles, we have:

\[
(6x - 6) + (4x - 14) = 180
\]

Now, combine like terms:

\[
6x + 4x - 6 - 14 = 180
\]
\[
10x - 20 = 180
\]

So, the correct equation to solve for \( x \) is:

\[
10x - 20 = 180
\]

This matches one of your provided options.