1. **State the problem:** We have a parallelogram with angles labeled as follows: top-right angle is $3x + 20$ degrees, bottom-left angle is $2y - 5$ degrees, and bottom-right angle is $x + 50$ degrees. We need to find the values of $x$ and $y$. 2. **Use the property of alternate interior angles:** Since the top-right angle $(3x + 20)^6$ and the bottom-right angle $(x + 50)^6$ are alternate interior angles formed by parallel lines, they are equal. 3. **Set up the equation for $x$:** $$3x + 20 = x + 50$$ 4. **Solve for $x$:** $$3x + 20 = x + 50$$ $$3x - \cancel{x} + 20 = \cancel{x} + 50$$ $$2x + 20 = 50$$ $$2x = 50 - 20$$ $$2x = 30$$ $$x = \frac{30}{2}$$ $$x = 15$$ 5. **Use the property of consecutive angles in a parallelogram:** Consecutive angles are supplementary, so the top-right angle $(3x + 20)^6$ and bottom-left angle $(2y - 5)^6$ add up to 180 degrees. 6. **Set up the equation for $y$:** $$ (3x + 20) + (2y - 5) = 180 $$ 7. **Substitute $x=15$ into the equation:** $$ (3(15) + 20) + (2y - 5) = 180 $$ $$ (45 + 20) + 2y - 5 = 180 $$ $$ 65 + 2y - 5 = 180 $$ $$ 60 + 2y = 180 $$ 8. **Solve for $y$:** $$ 2y = 180 - 60 $$ $$ 2y = 120 $$ $$ y = \frac{120}{2} $$ $$ y = 60 $$ **Final answers:** $$x = 15, \quad y = 60$$