Question

what is m∠prs? m∠prs=□° submit

Explanation:

Step1: Use the Angle Bisector Theorem (HL Congruence)

Since \(PS = PQ = 22\) and \(PR\) is a common side, and \(\angle PRS=\angle PRQ = 90^{\circ}\) (right angles), by the Hypotenuse - Leg (HL) congruence criterion for right - triangles \(\triangle PRS\cong\triangle PRQ\). So \(8a=a + 77\).

Step2: Solve the equation for \(a\)

Subtract \(a\) from both sides of the equation \(8a=a + 77\):
\(8a−a=a + 77−a\)
\(7a=77\)
Divide both sides by \(7\): \(a = 11\).

Step3: Find \(m\angle PRS\)

Substitute \(a = 11\) into the expression for \(\angle PRS\). Since \(\angle PRS=8a\), then \(m\angle PRS=8\times11=88^{\circ}\).

Answer:

\(88\)