Question

vertical angles are the opposite angles formed when two lines intersect. vertical angles do not share a side, and they have the same measure. which angle measures 50°? ∠jqk ∠kql ∠mqn ∠pqj

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. $\angle PQN = 50^{\circ}$, and $\angle JQK$ is vertical to $\angle PQN$.

Step2: Check other angles

$\angle KQL$ is adjacent to a right - angle and $\angle PQN$ (using linear - pair and right - angle properties, it's not $50^{\circ}$). $\angle MQN$ is a right - angle ($90^{\circ}$ as it's adjacent to a $50^{\circ}$ angle and forms a linear pair with a straight - line - related angle). $\angle PQJ$ is a straight - line angle minus $50^{\circ}$ (not $50^{\circ}$).

Answer:

$\angle JQK$