Question

in the figure, m∠3 = 75° and m∠10 = 105°. find the measure of ∠2.

Explanation:

Step1: Observe angle - angle relationships

Notice that $\angle3$ and $\angle10$ are supplementary ($75^{\circ}+ 105^{\circ}=180^{\circ}$). This implies that lines $w$ and $x$ are parallel (by the converse of the same - side interior angles postulate).

Step2: Identify corresponding angles

$\angle2$ and $\angle3$ are vertical angles.

Step3: Use vertical - angle property

Vertical angles are congruent. Since $m\angle3 = 75^{\circ}$, then $m\angle2=75^{\circ}$.

Answer:

$75^{\circ}$