1. **Stating the problem:** We are given a set of angles with relationships involving $x$, $2x$, $y$, and known angles $132^\circ$ and $47^\circ$ in a figure with parallel lines. 2. **Using the properties of parallel lines and angles:** - Angles on a straight line sum to $180^\circ$. - Alternate interior angles and corresponding angles are equal when lines are parallel. 3. **Calculate $x$ from the angle at B:** $$132^\circ + x = 180^\circ$$ $$x = 180^\circ - 132^\circ = 48^\circ$$ 4. **Calculate $y$ from the angle at C:** $$47^\circ + y = 180^\circ$$ $$y = 180^\circ - 47^\circ = 133^\circ$$ 5. **Use the sum of angles around point A:** $$2x + x + y = 180^\circ$$ Substitute $x=48^\circ$ and $y=133^\circ$: $$2(48) + 48 + 133 = 96 + 48 + 133 = 277^\circ$$ This exceeds $180^\circ$, so re-examine the problem. 6. **Re-examining the problem:** The sum of angles around a point on a straight line is $180^\circ$, so the equation should be: $$3x + 133 = 180$$ $$3x = 180 - 133 = 47$$ $$x = \frac{47}{3} \approx 15.67^\circ$$ 7. **Final answers:** - $x \approx 15.67^\circ$ - $y = 133^\circ$ These values satisfy the angle relationships given the parallel lines.