∠MAT

Question

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
?(1 point)
Responses

10x°−20°=180°
10 x minus 20 equals 180

10x°+20°=180°
10 x plus 20 equals 180

9x°−20°=180°
9 x minus 20 equals 180

x°−20°=180°

Answer 1

Since angles \( \angle MAT \) and \( \angle TAH \) are supplementary, their measures add up to \( 180^\circ \). Given the measures:

\[ \angle MAT = (6x - 6)^\circ \] \[ \angle TAH = (4x - 14)^\circ \]

We can set up the equation as follows:

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

Now combining like terms:

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

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

\[ 10x - 20 = 180 \]

The response is 10x°−20°=180°.