Question

lines b and c are parallel. what is the measure of ∠2? m∠2 = 31° m∠2 = 50° m∠2 = 120° m∠2 = 130°

Explanation:

Step1: Use the property of adjacent angles

Since lines \(b\) and \(c\) are parallel, \(\angle1=(7x + 1)^{\circ}\) and \(\angle2=(18x + 4)^{\circ}\) are adjacent angles on a straight - line. So \((7x + 1)+(18x + 4)=180\).

$$\begin{align*} 7x+1+18x + 4&=180\\ 25x+5&=180\\ 25x&=180 - 5\\ 25x&=175\\ x&=7 \end{align*}$$

Step2: Calculate the measure of \(\angle2\)

Substitute \(x = 7\) into \(\angle2=(18x + 4)^{\circ}\). Then \(\angle2=(18\times7+4)^{\circ}=(126 + 4)^{\circ}=130^{\circ}\)

Answer:

\(m\angle2 = 130^{\circ}\)