1. **State the problem:** We have a parallelogram EDFY with diagonals ED and FY. We need to find the values of $x$ and $y$ given the angle measures: - Angle at vertex F: $(7x - 5)^\circ$ - Angles at vertex Y: $45^\circ$ and $70^\circ$ - Angle at vertex D: $(5y)^\circ$ 2. **Recall properties of parallelograms:** - Opposite angles are equal. - Adjacent angles are supplementary (sum to $180^\circ$). - The sum of angles in any quadrilateral is $360^\circ$. 3. **Analyze angles at vertex Y:** The two marked angles at Y are $45^\circ$ and $70^\circ$, so the total angle at Y is: $$45 + 70 = 115^\circ$$ 4. **Use opposite angles equality:** Angle at D is opposite angle at F, so: $$(5y) = (7x - 5)$$ 5. **Use supplementary angles:** Angles at D and Y are adjacent, so: $$(5y) + 115 = 180$$ Simplify: $$5y = 180 - 115 = 65$$ $$y = \frac{65}{5} = 13$$ 6. **Find $x$ using the relation from step 4:** $$(5y) = (7x - 5)$$ Substitute $y=13$: $$5 \times 13 = 7x - 5$$ $$65 = 7x - 5$$ Add 5 to both sides: $$70 = 7x$$ Divide both sides by 7: $$x = 10$$ **Final answer:** $$x = 10, \quad y = 13$$