Chapter 4.6, Problem 3CYP

To determine

To calculate:

The value of each variable

Answer to Problem 3CYP

The value of variable $x$ and $y$ is $7°$ and $2$ units.

Explanation of Solution

Given information:

  

Calculation:

First label the figure as:

  

From figure, understands that:

  $\angle ACB$ is opposite to $\overline{AB}$

  $\angle ABC$ is opposite to $\overline{AC}$

Therefore,

  $\angle ABC\cong \angle ACB=\left(6x+8\right)°$

Know that:

The sum of all angles of triangle is $180°$

So,

  $\begin{array}{l}80°+\left(6x+8\right)°+\left(6x+8\right)°=180°\\ 12x=180°-80°-16°\\ 12x=84\\ x=7°\end{array}$

Now, the value of $y$ is calculated by using the congruent segments:

  $\begin{array}{l}\overline{AB}\cong \overline{AC}\\ 4y-2=2y+2\\ 2y=4\\ y=2\end{array}$