1. Problem statement: Find the measure of $\angle CAD$ in terms of $\angle 1$ and $\angle 2$ given that $\overline{BE}$ is parallel to $\overline{FH}$ and $\overline{AG}$ is a straight line. 2. Formula and rules: The Angle Addition Postulate says an angle can be written as the sum of two adjacent angles. Alternate interior and corresponding angles formed by parallel lines are equal. Angles on a straight line form a linear pair whose measures sum to 180 degrees. 3. Decompose the target angle using the Angle Addition Postulate: $\angle CAD = \angle CAE + \angle EAD$. 4. Use parallel-line angle relationships to identify equal angles: Because $\overline{BE} \parallel \overline{FH}$, the angle at $A$ that corresponds to $\angle 1$ is $\angle CAE$, so $\angle CAE = \angle 1$. Similarly, the angle at $A$ that corresponds to $\angle 2$ is $\angle EAD$, so $\angle EAD = \angle 2$. 5. Substitute these equalities into the decomposition: $\angle CAD = \angle 1 + \angle 2$. 6. Final answer: $\angle CAD = \angle 1 + \angle 2$.