Chapter 3.2, Problem 8WE

To determine

To find: the values of x and y .

Answer to Problem 8WE

  $x=10$

  $y=45$

Explanation of Solution

Given:

The diagram:

Concept Used:

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

Label the given figure as shown below:

Now, lines $\overline{AB}\parallel \overline{CD}$ and $\overline{BC}$ is a transversal, so by theorem 3-3,

  $m\angle DCB+m\angle CBA=180$ (Supplementary angles)

  $\begin{array}{c}2y+90=180\\ 2y=180-90\\ 2y=90\\ y=45\end{array}$

Similarly, lines $\overline{AB}\parallel \overline{CD}$ and $\overline{AD}$ is a transversal, so by theorem 3-3,

  $m\angle BAD+m\angle ADC=180$ (Supplementary angles)

  $\begin{array}{c}4x+14x=180\\ 18x=180\\ x=\frac{180}{18}\\ x=10\end{array}$