Question

current skill $ show answer (1) request help 2x + 142 9x + 126 4 3 1 6 7 8 find the measure of angle 1.

Explanation:

Step1: Identify the relationship between angles

Since the two lines are parallel, \(2x + 142\) and \(9x+126\) are same - side interior angles. Same - side interior angles are supplementary, so \((2x + 142)+(9x + 126)=180\).

Step2: Solve the equation for \(x\)

$$
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Step3: Find the measure of \(2x + 142\)

Substitute \(x =-8\) into \(2x + 142\): \(2\times(-8)+142=-16 + 142 = 126\).

Step4: Use the vertical - angle relationship

Angle \(1\) and \(2x + 142\) are vertical angles. Vertical angles are equal.

Answer:

\(126^{\circ}\)