Question

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

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: Simplify the equation

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

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

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

Answer:

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