Using Properties of Parallel Lines

Both angles are in the interior of the diagram and on opposite sides of the transversal. Therefore, they are alternate interior angles.

According to the Alternate Interior Angles Theorem, if the angles are congruent, then the lines are parallel.

\begin{gathered} 2x=5x-33^\circ \end{gathered}

Let's solve this equation.

2 x + = 5 x - 33

\text{LHS}-5 x=\text{RHS}-5 x

\text{-}3 x = \text{-} 33

\left.\text{LHS}\middle/(\text{-}3)\right.=\left.\text{RHS}\middle/(\text{-}3)\right.

x =11

When

x=11,

the lines

L_1

and

L_2

are parallel.

Using Properties of Parallel Lines 1.12 - Solution