Explanation
Step 1: Alternate interior angles) Let's see the following picture.
The head arrows on the segments DC and AB mean that both are parallel. Then, orange angles are alternate interior angles, which implies that both are equal. Then, we have
Step 2: Exterior angle theorem) Now, there is a very useful property of exterior angles. It says that every exterior angle of a triangle is the sum of its "opposite" interior angles:
In our present case, this theorem leads us to
[tex]5x=33+2x\text{.}[/tex]
Solving this equation for x, we get
[tex]\begin{gathered} 5x=33+2x, \\ 5x-2x=33, \\ 3x=33, \\ x=11. \end{gathered}[/tex]Answer[tex]x=11[/tex]
