Question

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

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, the angle with measure $(7x + 1)^{\circ}$ and the angle with measure $(18x+4)^{\circ}$ are related by the fact that they are vertical angles. So, $7x + 1=18x + 4$.

Step2: Solve the equation for $x$

Subtract $7x$ from both sides: $1 = 11x+4$. Then subtract 4 from both sides: $- 3=11x$. So, $x=-\frac{3}{11}$. This is incorrect. We should use the property of corresponding angles. Since lines $b$ and $c$ are parallel, the angles $(7x + 1)^{\circ}$ and $(18x + 4)^{\circ}$ are corresponding angles and are equal. So, $7x+1 = 18x + 4$. Rearranging gives $18x-7x=1 - 4$, $11x=-3$, $x = - \frac{3}{11}$ is wrong. It should be $7x+1+18x + 4=180$ (because they are same - side interior angles). Combining like terms: $25x+5 = 180$. Subtract 5 from both sides: $25x=175$. Divide both sides by 25: $x = 7$.

Step3: Find the measure of $\angle2$

The measure of $\angle2$ and the angle $(18x + 4)^{\circ}$ are vertical angles. Substitute $x = 7$ into $18x+4$. We get $18\times7+4=126 + 4=130^{\circ}$.

Answer:

$m\angle2 = 130^{\circ}$