Question

find the measure of the given angle.
if ( mangle lpn = 132^{circ} ) and ( mangle rpn = 37^{circ} ), find ( mangle 3 ).

Explanation:

Step1: Analyze the relationship between angles

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

Step2: Solve for \(m\angle3\)

Rearrange the formula: \(m\angle3=m\angle LPN - m\angle RPN\).
Substitute the given values: \(m\angle3 = 132^{\circ}-37^{\circ}\).
Calculate: \(m\angle3=95^{\circ}\).

Answer:

\(95^{\circ}\)