Chapter 5.2, Problem 27E

(a)

To determine

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

Answer to Problem 27E

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

  $x+y+90=180$

Explanation of Solution

Given:

  

Calculation:

Write an equation that represents the sum of the angle measures of the triangle.

  $x+y+90=180$

Conclusion:

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

  $x+y+90=180$

(b)

To determine

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

Answer to Problem 27E

The values of $x$ and $y$ are

  $\begin{array}{l}x=67°\\ y=23°\end{array}$

Explanation of Solution

Calculation:

Solve the system:

  $\begin{array}{l}\{\begin{array}{l}x+y+90=180\\ x+2=3y\end{array}\\ \{\begin{array}{l}x+y=180-90\\ x=3y-2\end{array}\\ \{\begin{array}{l}x+y=90\\ x=3y-2\end{array}\\ \left(3y-2\right)+y=90\\ 4y-2=90\\ 4y=92\\ y=23\\ x=3.23-2\\ x=69-2\\ x=67\end{array}$

The solution is:

  $\begin{array}{l}x=67°\\ y=23°\end{array}$

Conclusion:

The values of $x$ and $y$ are

  $\begin{array}{l}x=67°\\ y=23°\end{array}$