1. **Stating the problem:** We have two parallel horizontal lines intersected by two parallel diagonal lines, creating several angles. We want to find which angle facts can be used to find angle $g$ and then angle $h$ from $g$. 2. **Angle fact to find angle $g$:** Since the two diagonal lines are parallel and intersected by the horizontal lines, angle $g$ and the given $137^\circ$ angle are corresponding angles formed by a transversal cutting parallel lines. **Corresponding angles are equal when lines are parallel.** Therefore, angle $g = 137^\circ$. 3. **Angle fact to find angle $h$ from angle $g$:** Angle $h$ and angle $g$ lie on the same side of the transversal and are interior angles between the two parallel horizontal lines. **Consecutive interior angles (also called co-interior or same-side interior angles) are supplementary, meaning their sum is $180^\circ$.** So, we use the formula: $$h + g = 180^\circ$$ 4. **Calculate angle $h$:** $$h = 180^\circ - g = 180^\circ - 137^\circ = 43^\circ$$ **Summary:** - To find $g$, use the Corresponding Angles Postulate. - To find $h$ from $g$, use the Consecutive Interior Angles Theorem. Final answers: $$g = 137^\circ$$ $$h = 43^\circ$$