Chapter 4.2, Problem 37PPS

To determine

The measure of the numbered angles.

Answer to Problem 37PPS

  $m\angle 2=20°$

  $m\angle 5=110°$

  $m\angle 5=70°$

  $m\angle 4=40°$

  $m\angle 8=m\angle 1=65°$

  $m\angle 3=95°$

  $m\angle 6=45°$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

The sum of acute angle of a right triangle is 90 degrees. The sum of the measures of the angles of a triangle is 180 degrees.

The value of angle 2 will be:

  $\begin{array}{l}m\angle 2=180°-130°-30°\\ m\angle 2=20°\end{array}$

The value of angle 5 will be:

  $m\angle 5=110°$

The value of angle 7 will be:

  $\begin{array}{l}m\angle 5=180°-110°\\ m\angle 5=70°\end{array}$

The value of angle 4 will be:

  $\begin{array}{l}m\angle 4=180°-m\angle 5-30°\\ m\angle 4=180°-110-30°\\ m\angle 4=40°\end{array}$

The value of angle 1 will be:

  $\begin{array}{l}m\angle 1+m\angle 8=130°\\ m\angle 1+m\angle 1+m\angle 1=130°\\ m\angle 1=65°\\ \text{Thus,}\\ m\angle 8=m\angle 1=65°\end{array}$

The value of angle 3 will be:

  $\begin{array}{l}m\angle 3=180-m\angle 1-m\angle 2\\ m\angle 3=180-65-20\\ m\angle 3=95°\end{array}$

The value of angle 6 will be:

  $\begin{array}{l}m\angle 6=110-m\angle 8\\ m\angle 6=110-65\\ m\angle 6=45°\end{array}$