Chapter 4.2, Problem 1BCYP

To determine

The value of each angle.

Answer to Problem 1BCYP

  $\begin{array}{l}m\angle 7=57°\\ m\angle 5=33°\\ m\angle 4=56°\\ m\angle 6=123°\\ m\angle 8=m\angle 9=28.5°\end{array}$

Explanation of Solution

Given:

The given figure is:

Calculation:

The sum of the angles in a triangle is 180 degrees. Therefore,

  $\begin{array}{l}m\angle 7+65+58=180\\ m\angle 7=180-65-58\\ m\angle 7=57°\end{array}$

Angle 7 and 5 are vertically opposite, therefore,

  $m\angle 5=m\angle 7=57°$

The sum of the angles in a triangle is 180 degrees. Therefore,

  $\begin{array}{l}m\angle 4+57+67=180\\ m\angle 4=180-67-57\\ m\angle 4=56°\end{array}$

Angle 5 and 6 are supplementary, therefore,

  $\begin{array}{l}m\angle 6+m\angle 5=180\\ m\angle 6=180-57\\ m\angle 6=123\end{array}$

Angles 8 and 9 are equal. The sum of the angles in a triangle is 180 degrees. Therefore,

  $\begin{array}{l}m\angle 8+m\angle 9+123=180\\ 2m\angle 8=180-123\\ m\angle 8=m\angle 9=\frac{57°}{2}=28.5°\end{array}$