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

Step2: Solve the equation for \(x\)

Combine like terms: \(7x+18x+1 + 4=180\), \(25x+5 = 180\). Subtract \(5\) from both sides: \(25x=180 - 5=175\). Divide both sides by \(25\): \(x=\frac{175}{25}=7\).

Step3: Find the measure of \(\angle2\)

Substitute \(x = 7\) into the expression for \(\angle2\): \(\angle2=(18x+4)^{\circ}\). So, \(\angle2=(18\times7 + 4)^{\circ}=(126+4)^{\circ}=130^{\circ}\).

Answer:

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