Question

what is $m\angle qps$?
$m\angle qps=\square{}^{circ }$

Explanation:

Step1: Recall the total degrees in a circle

A full - circle has \(360^{\circ}\).

Step2: Set up the equation

Let \(m\angle QPS=x\). We know that \(x + 131^{\circ}+89^{\circ}+90^{\circ}=360^{\circ}\) (the un - labeled angle is \(90^{\circ}\) since the sum of angles around a point \(P\) in a circle is \(360^{\circ}\)).

Step3: Simplify the left - hand side of the equation

\(x+(131 + 89+90)^{\circ}=360^{\circ}\). First, calculate \(131 + 89+90=(131 + 89)+90=220 + 90 = 310^{\circ}\). So the equation becomes \(x+310^{\circ}=360^{\circ}\).

Step4: Solve for \(x\)

Subtract \(310^{\circ}\) from both sides of the equation: \(x=360^{\circ}-310^{\circ}\).

Answer:

\(50\)