1. **Stating the problem:** We have a parallelogram with two given angle measures expressed in terms of $x$: one angle is $4x - 50^\circ$ and the adjacent angle is $x + 20^\circ$. We need to form an equation in $x$ and find the numerical measure of each angle. 2. **Important properties of parallelograms:** - Opposite angles are equal. - Adjacent angles are supplementary, meaning their sum is $180^\circ$. 3. **Forming the equation:** Since the two given angles are adjacent, their sum must be $180^\circ$: $$ (4x - 50) + (x + 20) = 180 $$ 4. **Simplify the equation:** $$ 4x - 50 + x + 20 = 180 $$ $$ 5x - 30 = 180 $$ 5. **Solve for $x$:** $$ 5x = 180 + 30 $$ $$ 5x = 210 $$ $$ x = \frac{210}{5} = 42 $$ 6. **Find each angle measure:** - First angle: $4x - 50 = 4(42) - 50 = 168 - 50 = 118^\circ$ - Second angle: $x + 20 = 42 + 20 = 62^\circ$ 7. **Check:** $118^\circ + 62^\circ = 180^\circ$, confirming the solution is correct. **Final answer:** The angles of the parallelogram are $118^\circ$ and $62^\circ$.