Question

find the measure of the given angle.
if ( mangle mpn = 32^{circ} ) and ( mangle 3 = 89^{circ} ), find ( mangle rpn ).

Explanation:

Step1: Analyze the relationship between angles

We know that \(m\angle3=m\angle MPN + m\angle RPN\) (angle addition postulate).

Step2: Solve for \(m\angle RPN\)

Rearrange the formula: \(m\angle RPN=m\angle3 - m\angle MPN\).
Substitute the given values: \(m\angle RPN = 89^{\circ}-32^{\circ}\).
Calculate: \(m\angle RPN=57^{\circ}\).

Answer:

\(57^{\circ}\)