Question

solve for ( mangle opr ) if ( mangle opq = 115^{circ} ) and ( mangle rpq = 75^{circ} ).

Explanation:

Step1: Use the angle - subtraction formula

We know that \(m\angle OPQ=m\angle OPR + m\angle RPQ\). So, we can rewrite the formula to solve for \(m\angle OPR\) as \(m\angle OPR=m\angle OPQ - m\angle RPQ\).

Step2: Substitute the given values

Given \(m\angle OPQ = 115^{\circ}\) and \(m\angle RPQ=75^{\circ}\). Substitute these values into the formula: \(m\angle OPR = 115^{\circ}-75^{\circ}\).

Step3: Calculate the result

\(115 - 75=40\), so \(m\angle OPR = 40^{\circ}\).

Answer:

\(40\)