Chapter 11.1, Problem 24PPS

To determine

To find:The value of $x,m\angle 1\text{ and }m\angle 5$ if $m\angle 1=5x\text{}\text{ and }m\angle 5=2x-2$

Answer to Problem 24PPS

The value of $x=26°,m\angle 1=130°\text{ and }m\angle 5=50°$ .

Explanation of Solution

Given:

The figure of parallel lines and transversal line is shown below in Figure 1.

  

Figure 1

Calculation:

It can be seen from Figure 1 that the line a is parallel to line band the line z is transversal line.

It can be seen from Figure 1 that $m\angle 1\text{ and }m\angle 5$ are linear pairs that means the sum of $m\angle 1\text{ and }m\angle 5$ is $180°$ .

Add $m\angle 1=5x\text{}\text{ and }m\angle 5=2x-2$ and equate with $180°$ to obtain the value of $x$ .

  $\begin{array}{c}m\angle 1\text{}\text{ +}m\angle 5=180°\\ 5x+2x-2=180\\ 7x-2=180\\ 7x=180+2\end{array}$

Further simplify the above calculation.

  $\begin{array}{c}7x=182\\ x=\frac{182}{2}\\ x=26\end{array}$

Therefore, the value of $x=26°$ .

Now substitute $x=26°$ in $m\angle 1=5x\text{}$ to obtain the value of $m\angle 1$ .

  $\begin{array}{l}m\angle 1=5\left(26°\right)\\ m\angle 1=130°\end{array}$

Now substitute $x=26°$ in $m\angle 5=2x-2$ to obtain the value of $m\angle 5$ .

  $\begin{array}{c}m\angle 5=2\left(26°\right)-2\\ =52°-2\\ =50°\end{array}$

Therefore, the value of $m\angle 1=130°\text{ and }m\angle 5=50°$ .

Conclusion:

Thus, the value of $x=26°,m\angle 1=130°\text{ and }m\angle 5=50°$ .