Question

solve for the missing angles in the two diagrams below.

Explanation:

Step1: Identify angle - relationship in left diagram

The two lines are parallel and the angles are corresponding.
So $x = 83^{\circ}$

Answer:

In the left - hand diagram, $x = 83^{\circ}$. In the right - hand diagram, all the angles are already given ($83^{\circ}$ and $97^{\circ}$ pairs as shown), and no missing angles need to be solved for.