Chapter 6.2, Problem 34PPS

To determine

The measure of angle DAC from the given figure.

Answer to Problem 34PPS

  $m\angle DAC=72$

Explanation of Solution

Given:

The given figure is:

Calculation:

Angles AFB and BFC make a linear pair in the given figure.

According to the Supplementary Angles Theorem, angles AFB and BFC are supplementary.

So,

  $\begin{array}{l}m\angle AFB+m\angle BFC=180\\ m\angle AFB+49=180\\ m\angle AFB=180-49\\ m\angle AFB=131\end{array}$

According to the Exterior Angle Theorem, the measure of an exterior angle of triangle is equal to the sum of measures of the two remote interior angles.

So, in triangle DAF;

  $\begin{array}{l}m\angle DAC+m\angle ADF=m\angle AFB\\ m\angle DAC+59=131\\ m\angle DAC=131-59\\ m\angle DAC=72\end{array}$