Chapter 6.2, Problem 35PPS

To determine

The measure of angle ACD from the given figure.

Answer to Problem 35PPS

  $m\angle ACD=29$

Explanation of Solution

Given:

The given figure is:

Calculation:

In the given figure, according to the definition of a parallelogram, sides AB and CD are parallel to each other.

Therefore, by Alternate Angles Theorem,

  $m\angle CDB=m\angle ABD=20$

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 DFC;

  $\begin{array}{l}m\angle CDB+m\angle ACD=m\angle BEC\\ 20+m\angle ACD=49\\ m\angle ACD=49-20\\ m\angle ACD=29\end{array}$