Chapter 12.1, Problem 56E

To determine

To find: the measurement of segment $GH$ from the given diagram.

Answer to Problem 56E

  $GH=12.$

Explanation of Solution

Given:

  

Concept used:

If two angles are congruentthen their side will be same.

Congruent can be check by using distance formula in each side.

The unknown side can be measured by equating its side.

Calculation:

On the diagram it is clearly seen that the line segment $\overline{GH}$ and $\overline{BA}$ are congruent.

  $\begin{array}{l}GH=BA\\ 3y=5y-8.\\ -2y=-8.\\ y=4.\end{array}$

By putting the value of $y$ in the given angle:

  $GH=3\left(4\right)=12$ .

Hence, $GH=12.$