lines b and c are parallel. what is the measure of $ \angle 2 $? $ m \angle 2 = 31 ^ { \circ } $ $ m \angle 2 = 50 ^ { \circ } $ $ m \angle 2 = 120 ^ { \circ } $ $ m \angle 2 = 130 ^ { \circ } $

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Accepted Answer

# Explanation:
## Step1: Use the property of consecutive interior angles
Since lines $b$ and $c$ are parallel, $(7x + 1)+(18x+4)=180$ (consecutive interior angles are supplementary).
$$
\begin{align*}
7x+1 + 18x+4&=180\
25x+5&=180\
25x&=180 - 5\
25x&=175\
x&=7
\end{align*}
$$
## Step2: Find the measure of $\angle2$
Substitute $x = 7$ into $(18x + 4)$
$$
\begin{align*}
18x+4&=18\times7+4\
&=126 + 4\
&=130
\end{align*}
$$

# Answer:
$\text{m}\angle2 = 130^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of consecutive interior angles

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

Answer: