Question

first, find ( mangle jqk ).
( mangle jqk = 70^circ )
now, find ( mangle mqn ).
( mangle mqn = )

Explanation:

Step1: Calculate the sum of known angles

The sum of angles around a point is \(360^{\circ}\).
The known angles are \(80^{\circ}+70^{\circ}+30^{\circ}\).

$$80 + 70+30=180^{\circ}$$

Step2: Find \(m\angle MQN\)

Let \(m\angle MQN = x\).
Since the sum of all angles around point \(Q\) is \(360^{\circ}\), and we know that \(x + 180^{\circ}=360^{\circ}\) (because the other three - angle sum is \(180^{\circ}\) and the total is \(360^{\circ}\)).

$$x=360 - 180$$

$$x = 120^{\circ}$$

Answer:

\(120\)