Question

current skill
show answer request h
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-9x + 171
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7
6x + 39
find the measure of angle 7.

Explanation:

Step1: Use the property of parallel lines and transversal

Since the two lines are parallel, \(-9x + 171\) and \(6x+39\) are supplementary. So, \((-9x + 171)+(6x + 39)=180\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation: \(-9x+171 + 6x+39=-3x + 210\).
Set \(-3x + 210 = 180\).
Subtract 210 from both sides: \(-3x=180 - 210=-30\).
Divide both sides by \(-3\): \(x = 10\).

Step3: Find the measure of \(\angle7\)

Substitute \(x = 10\) into \(6x+39\): \(6\times10+39=60 + 39=99\).
\(\angle7\) and \(6x + 39\) are vertical angles. Vertical angles are equal.

Answer:

\(99^{\circ}\)