Chapter 3, Problem 19CUR

To determine

To find: the measure of $\angle DHC$

Answer to Problem 19CUR

The angle $\angle DHC={60}^0$

Explanation of Solution

Given information:

The given figure is as follows

  $\angle AHD={60}^0,\overleftrightarrow{AB}\perp \overline{GH},\overleftrightarrow{AB}\parallel \overleftrightarrow{CD}$

  $\overleftrightarrow{AB}$ bisects $\angle DHF$

Calculation:

From the given data,

  $\angle AHF=\angle AHD={60}^0$ . Since, $\overleftrightarrow{AB}$ Bisects

  $\angle DHF$

  $\begin{array}{l}\angle DHC=180-\angle AHF-\angle AHD\\ =180-60-60\\ =60\end{array}$

Hence, the angle $\angle DHC={60}^0$