Question

find the measure of the given angle.
if ( mangle mpn = 39^{circ} ) and ( mangle rpn = 54^{circ} ), find ( mangle 3 ).

Explanation:

Step1: Recall the sum of angles around a point

The sum of angles around a point \(P\) is \(360^{\circ}\).

Step2: Set up the equation

We know that \(m\angle MPN + m\angle RPN+m\angle3 = 360^{\circ}- 180^{\circ}\) (since \(\angle MPL\) is a straight - line adjacent to the angles we are considering).
Substituting the given values: \(39^{\circ}+54^{\circ}+m\angle3 = 180^{\circ}\)

Step3: Solve for \(m\angle3\)

First, add \(39^{\circ}\) and \(54^{\circ}\): \(39 + 54=93\).
Then, \(m\angle3=180^{\circ}-93^{\circ}\)
\(m\angle3 = 87^{\circ}\)

Answer:

\(87^{\circ}\)