Question

find the measure of the given angle.
find ( mangle rpn ) if ( mangle mpn = 35^{circ} ) and ( mangle 3 = 90^{circ} ).

Explanation:

Step1: Use the angle - sum relationship

We know that \(\angle MPN+\angle RPN = \angle 3\) (because they are adjacent angles that form \(\angle3\)).

Step2: Solve for \(\angle RPN\)

Let \(x = m\angle RPN\). Given \(m\angle MPN=35^{\circ}\) and \(m\angle3 = 90^{\circ}\).
From the equation \(x + 35^{\circ}=90^{\circ}\), we can find \(x\) by subtracting \(35^{\circ}\) from both sides.
\(x=90^{\circ}- 35^{\circ}\)

Answer:

\(55^{\circ}\)