Solve Equations with Supplementary Angles Quick Check

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Question
∠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
?(1 point)
Responses

9x°−20°=180°
9 x minus 20 equals 180

x°−20°=180°
x minus 20 equals 180

10x°+20°=180°
10 x plus 20 equals 180

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

To find an equation for \(x\) based on the measures of the supplementary angles \(\angle MAT\) and \(\angle TAH\), we need to set up the equation based on the fact that supplementary angles sum up to \(180^\circ\).

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

Since the angles are supplementary, we can write the equation: \[ (6x - 6) + (4x - 14) = 180 \]

Now, we simplify this equation: \[ 6x - 6 + 4x - 14 = 180 \] \[ 10x - 20 = 180 \]

Thus, the equation to solve for \(x\) is: \[ 10x - 20 = 180 \]

Therefore, the correct response from your options is: 10x°−20°=180°.