Question

lines r and s are parallel. find the value of x, then find the measure of
m∠1=(79−2x)°
m∠2=(92−3x)°

x=
(type an integer or a fraction.)

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Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(79 - 2x)^{\circ}\) and \(m\angle2=(92 - 3x)^{\circ}\) into the equation:
\((79 - 2x)+(92 - 3x)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(79+92-2x - 3x=180\)
\(171-5x = 180\)

Step3: Solve for \(x\)

Subtract 171 from both sides:
\(-5x=180 - 171\)
\(-5x=9\)
Divide both sides by \(-5\):
\(x=\frac{9}{-5}=- \frac{9}{5}\)

Answer:

\(-\frac{9}{5}\)