Question

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

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 the given expressions: \((79 - 2x)+(92 - 3x)=180\).

Step2: Simplify the equation

Combine like - terms: \(79+92-2x - 3x=180\), which simplifies to \(171-5x = 180\).

Step3: Solve for \(x\)

Subtract 171 from both sides: \(-5x=180 - 171\), so \(-5x = 9\). Then divide both sides by \(-5\): \(x=-\frac{9}{5}=- 1.8\).

Step4: Find \(m\angle1\)

Substitute \(x = - 1.8\) into \(m\angle1=(79 - 2x)^{\circ}\).
\(m\angle1=79-2\times(-1.8)=79 + 3.6=82.6^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x=-1.8\) into \(m\angle2=(92 - 3x)^{\circ}\).
\(m\angle2=92-3\times(-1.8)=92 + 5.4 = 97.4^{\circ}\).

Answer:

\(x=-1.8\), \(m\angle1 = 82.6^{\circ}\), \(m\angle2=97.4^{\circ}\)