1. **State the problem:** We have a quadrilateral with the top and bottom sides parallel. On the right side, two angles are labeled: the top angle is $x^\circ$ and the bottom angle is $(x - 56)^\circ$. The bottom-left corner is a right angle ($90^\circ$). We need to find the value of $x$ and the measure of each labeled angle. 2. **Identify the key property:** Since the top and bottom sides are parallel, the angles on the right side are consecutive interior angles formed by a transversal. Consecutive interior angles are supplementary, meaning their sum is $180^\circ$. 3. **Set up the equation:** $$x + (x - 56) = 180$$ 4. **Simplify the equation:** $$2x - 56 = 180$$ 5. **Add 56 to both sides:** $$2x - \cancel{56} + 56 = 180 + 56$$ $$2x = 236$$ 6. **Divide both sides by 2:** $$\frac{2x}{\cancel{2}} = \frac{236}{2}$$ $$x = 118$$ 7. **Find the measure of each labeled angle:** - Top angle: $x = 118^\circ$ - Bottom angle: $x - 56 = 118 - 56 = 62^\circ$ **Final answer:** - $x = 118^\circ$ - Top angle = $118^\circ$ - Bottom angle = $62^\circ$