Question

in the figure, m∠3 = 75° and m∠10 = 105°. find the measure of ∠14.

Explanation:

Step1: Identify angle - pair relationship

$\angle3$ and $\angle10$ are supplementary since $m\angle3 = 75^{\circ}$ and $m\angle10=105^{\circ}$ ($75 + 105=180^{\circ}$), which implies that the lines are parallel.

Step2: Locate $\angle10$ and $\angle14$

$\angle10$ and $\angle14$ are vertical angles.

Step3: Use vertical - angle property

Vertical angles are congruent. So $m\angle14=m\angle10$.

Answer:

$105^{\circ}$