Chapter 5, Problem 15CUR

To determine

To find: the measures of the angles.

Answer to Problem 15CUR

$150°$ And $150°$

Explanation of Solution

Given:

Two parallel lines are cut by transversal, a pair of corresponding angles have measures $2x+50$ and $3x$ .

From the postulate 10, corresponding angles having measures $2x+50$ and $3x$ are congruent.

That is,

  $\begin{array}{c}2x+50=3x\\ 50=3x-2x\\ 50=x\end{array}$

Now, substitute $x=50$ in the measure of first angle $2x+50$ ,

  $\begin{array}{c}2x+50=2\left(50\right)+50\\ =100+50\\ =150\end{array}$

Now, substitute $x=50$ in the measure of second angle $3x$ ,

  $\begin{array}{c}3x=3\left(50\right)\\ =150\end{array}$

Hence, the two required angles are $150°$ and $150°$