Question

if line m || line n and ∠2 measures 35°, what is the measure of ∠5?
o 55°
o 155°
o 145°
o 180°

Explanation:

Step1: Identify angle - pair relationship

$\angle2$ and $\angle4$ are vertical angles.
Since vertical angles are equal, $m\angle4 = m\angle2=35^{\circ}$.

Step2: Use property of parallel lines

Lines $m$ and $n$ are parallel. $\angle4$ and $\angle5$ are same - side interior angles.
Same - side interior angles are supplementary, so $m\angle4 + m\angle5=180^{\circ}$.

Step3: Solve for $m\angle5$

Substitute $m\angle4 = 35^{\circ}$ into $m\angle4 + m\angle5=180^{\circ}$.
We get $35^{\circ}+m\angle5 = 180^{\circ}$.
Then $m\angle5=180^{\circ}- 35^{\circ}=145^{\circ}$.

Answer:

C. $145^{\circ}$