Chapter 7.3, Problem 14IP

To determine

Find the actual angle measures of the Triangle.

Answer to Problem 14IP

The actual measurements of the angles are: ${50}^0,{60}^0,{70}^0$

Explanation of Solution

Given:

The angle measures of the triangle are: ${(x+15)}^0;{(2x-10)}^0;2x^0$

Concept Used:

Sum of 3 angles of Triangle is ${180}^0$

According to the condition: ${(x+15)}^0+{(2x-10)}^0+2x^0={180}^0$

Calculation:

Sum of 3 angles of Triangle is ${180}^0$

According to the condition: ${(x+15)}^0+{(2x-10)}^0+2x^0={180}^0$

Now solve for x:

  $\begin{array}{l}(x+15)+(2x-10)+2x=180\\ (x+2x+2x)+(15-10)=180\\ 5x+5=180\\ 5x+5-5=180-5[\text{Subtract}\text{5}\text{from}\text{both}\text{side}s]\\ 5x=175\\ \frac{5x}{5}=\frac{175}{5}[\text{Divide}\text{each}\text{side}\text{by}5]\\ x=35\end{array}$

Measurement of each angle:

  $\begin{array}{l}$ {(x+15)}^0={(35+15)}^0={50}^0$$ {(2x-10)}^0={(2·35-10)}^0={60}^0$2x^0=2·35{}^0={70}^0\end{array}$ Measurements of the angles are: ${50}^0,{60}^0,{70}^0$

Thus, measurements of the angles are: ${50}^0,{60}^0,{70}^0$