∠MAT and ∠TAH are supplementary angles. The angles have the following measures: ∡MAT=(6x−6)° and ∡TAH=(4x−14)° . What is an equation to solve for x ? Please solve

Answer 1

Since \( \angle MAT \) and \( \angle TAH \) are supplementary angles, their sum equals \( 180^\circ \). Therefore, we can write the equation:

\[ \angle MAT + \angle TAH = 180^\circ \]

Substituting the given expressions for the angles:

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

Now, combine like terms:

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

This simplifies to:

\[ 10x - 20 = 180 \]

Next, add \( 20 \) to both sides of the equation:

\[ 10x = 200 \]

Now, divide both sides by \( 10 \):

\[ x = 20 \]

Thus, the solution for \( x \) is:

\[ \boxed{20} \]