Chapter 4.2, Problem 2CYU

To determine

The measure of the numbered angle.

Answer to Problem 2CYU

  $m\angle 1=42°$

  $m\angle 2=39°$

  $m\angle 3=51°$

Explanation of Solution

Given:

The given figure is:

Calculation:

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

  $\begin{array}{l}m\angle 1+90+48=180\\ m\angle 1+138=180\\ m\angle 1=180-38\\ m\angle 1=42°\end{array}$

Angle 3 and angle FDE are complimentary angles. Therefore,

  $\begin{array}{l}m\angle 3+\angle FDE=90\\ m\angle 3+39=90\\ m\angle 3=90-39\\ m\angle 3=51°\end{array}$

Angle 2 and angle FDE are alternate interior angles. Therefore,

  $\begin{array}{l}m\angle 2=\angle FDE\\ m\angle 2=39°\end{array}$