Question

first, find ( mangle jqk ). ( mangle jqk=square )

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. $\angle JQP$ and $\angle LQK$ are vertical angles.
Since $\angle JQP = 80^{\circ}$, then $\angle LQK=80^{\circ}$

Step2: Calculate $m\angle JQK$

We know that $\angle JQK+\angle KQL=\angle JQL$. Also, $\angle JQL = 180^{\circ}$ (a straight - line angle). Given $\angle KQL = 30^{\circ}$
$m\angle JQK=180^{\circ}-\angle KQL$
Substitute $\angle KQL = 30^{\circ}$ into the formula: $m\angle JQK = 180 - 30$

Answer:

$150$