Question

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

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. The angle adjacent to \(80^{\circ}\) and \(30^{\circ}\) forms a linear - pair with \(\angle JQK\). But we can also note that \(\angle JQK\) and the angle composed of \(80^{\circ}\) and \(30^{\circ}\) are vertical angles.
The sum of angles around a point is \(180^{\circ}\), but for vertical angles, we know that \(\angle JQK\) is equal to the sum of the non - adjacent angles.

$$m\angle JQK=80^{\circ}+30^{\circ}$$

Step2: Calculate the sum

$$m\angle JQK = 110^{\circ}$$

Answer:

\(110\)