Chapter 4.2, Problem 36PPS

To determine

The measure of the numbered angles.

Answer to Problem 36PPS

  $\begin{array}{l}m\angle 1=55°\\ m\angle 3=55°\\ m\angle 2=75°\\ m\angle 4=15°\end{array}$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

The sum of acute angle of a right triangle is 90 degrees.

The value of angle 1 will be:

  $\begin{array}{l}m\angle 1=90°-35°\\ m\angle 1=55°\end{array}$

The value of angle 3 will be:

  $\begin{array}{l}m\angle 3=90°-35°\\ m\angle 3=55°\end{array}$

The sum of the measures of the angles of a triangle is 180 degrees.

  $\begin{array}{l}m\angle 2+70+35=180\\ m\angle 2+105=180\\ m\angle 2=180-105\\ m\angle 2=75°\end{array}$

The sum of acute angle of a right triangle is 90 degrees.

  $\begin{array}{l}m\angle 4=90-m\angle 2\\ m\angle 4=90-75\\ m\angle 4=90-75\\ m\angle 4=15°\end{array}$