Question

in the diagram, lines m and n are parallel, and the angles have the measures shown. what is m∠1 in degrees? (3x + 2)° (5x + 18)°

Explanation:

Step1: Use angle - relationship of parallel lines

Since lines \(m\) and \(n\) are parallel, the angles \((5x + 18)^{\circ}\) and \((3x+2)^{\circ}\) are supplementary. So, \((5x + 18)+(3x + 2)=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(5x+3x+18 + 2=180\), which simplifies to \(8x+20 = 180\). Subtract 20 from both sides: \(8x=180 - 20=160\). Then divide both sides by 8: \(x=\frac{160}{8}=20\).

Step3: Find the measure of one of the angles

Substitute \(x = 20\) into \((3x + 2)\): \(3x+2=3\times20 + 2=60 + 2=62^{\circ}\).

Step4: Find the measure of \(\angle1\)

\(\angle1\) and the angle \((3x + 2)^{\circ}\) are vertical angles. Vertical angles are equal. So \(m\angle1=(3x + 2)^{\circ}\). Since \(x = 20\), \(m\angle1=62^{\circ}\).

Answer:

\(62^{\circ}\)