Chapter 6.6, Problem 74SPR

To determine

The measure of angle MHG.

Answer to Problem 74SPR

  $m\angle MHG=31$

Explanation of Solution

Given:

DFGH is a rhombus.

  

  $m\angle FGH=118$

Calculation:

Rhombus has four congruent sides.

Hence, $\overline{GH}\cong \overline{GF}.$

In the triangle GHF, according to Isosceles Triangle Theorem, the measure of angle GHF is equal to the measure of angle GFH.

The sum of the angles of a triangle is 180.

In triangle GHF;

  $\begin{array}{l}m\angle FGH+m\angle MFG+m\angle MHG=180\\ 118+m\angle MHG+m\angle MHG=180\\ 118+2\left(m\angle MHG\right)=180\\ 2\left(m\angle MHG\right)=62\\ m\angle MHG=31\end{array}$