Question

what is $mangle qps$?
$mangle qps=square^{circ}$

Explanation:

Step1: Use the property of full - angle in a circle

The sum of angles around a point in a circle is \(360^{\circ}\). So, \((x + 76)+80+(4x-86)=360\).

Step2: Simplify the equation

Combine like terms: \(x+76 + 80+4x-86=360\), which becomes \(5x + 70=360\).

Step3: Solve for \(x\)

Subtract \(70\) from both sides: \(5x=360 - 70=290\). Then divide by \(5\): \(x=\frac{290}{5}=58\).

Step4: Find \(m\angle QPS\)

Since \(m\angle QPS=x + 76\), substitute \(x = 58\) into it. So, \(m\angle QPS=58+76\).

Answer:

\(134\)