Chapter 12.1, Problem 57E

To determine

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

Answer to Problem 57E

  $BC=15.$

Explanation of Solution

Given:

  

Concept used:

If two angles are congruent then their side will be same.

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

The side can be measured by equating its unknown value of side.

Calculation:

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

  $\begin{array}{l}BC=HK\\ 3z+6=8z-9.\\ -5z=-15.\\ z=3.\end{array}$

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

  $BC=3\left(z\right)+6=3\left(3\right)+6=15.$ .

Hence, $BC=15.$