Chapter 5.2, Problem 28E

(a)

To determine

To find: the sum of the angle measures of the triangle.

Answer to Problem 28E

Hence, the sum of the angle measures of the triangle is:

  $x+2y=198$

Explanation of Solution

Given:

  

Calculation:

The sum of the interior angles of a triangle is $180°$ so we can write:

  $x+y+\left(y-18\right)=180$

Simplify:

  $x+2y=198$

Conclusion:

Hence, the sum of the angle measures of the triangle is:

  $x+2y=198$

(b)

To determine

To find: the values of $x$ and $y$ .

Answer to Problem 28E

The values of $x$ and $y$ are

  $x=86,y=56$

Explanation of Solution

Calculation:

Let:

  $\begin{array}{l}x+2y=198\leftarrow \text{Eq}\text{.1}\\ \text{3x-5y=-22 }\leftarrow \text{Eq}\text{.2}\end{array}$

Solve for one variable in using eq. $\text{1}$ :

  $x=198-2y$

Substitute on eq. $\text{2}$ :

  $3\left(198-2y\right)-5y=-22$

Simplify & solve for $y$ :

  $\begin{array}{l}594-6y-5y=-22\\ -11y=-616\\ \text{y=56}\end{array}$

Solve for $\text{x}$ :

  $\begin{array}{l}x=198-2\left(56\right)\\ \text{x=86}\end{array}$

The solution is:

  $x=86,y=56$

Conclusion:

The values of $x$ and $y$ are

  $x=86,y=56$