Question

Complete the following statement.

When two parallel lines are cut by a transversal, a pair of corresponding angles have measure $2x+50$ and $3x$. The measures of the angles are __ and __?

Short answer

The measure of the angles is ${150}^{\circ },{150}^{\circ }$.

Step-by-step solution

Step 2- Apply the concept of the alternate interior angle property.

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Step 2- Step description.

Sinceangles the congruent thus simplify the equations as follows:

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

Substitute 50 for x in$2x+50$ and3X and simplify further.

Step 3- Step description.

Simplify as follows:

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

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

Therefore, the measures of the angles is ${150}^{\circ }$,.${150}^{\circ }$