In the diagram, we need to find the values of angles $x$ and $y$.

1. For angle $x$: Notice that $x$ is a vertical angle with the 31° angle provided in the diagram. Vertical angles are always equal, so: $x = 31^\circ$

2. For angle $y$: The angle $y$ is part of a linear pair with the 31° angle, which means they form a straight line and must sum to 180° (since a straight line measures 180°). Thus: $y + 31^\circ = 180^\circ$ Solving for $y$: $y = 180^\circ - 31^\circ = 149^\circ$

So, the missing angles are:

• $x = 31^\circ$
• $y = 149^\circ$

Would you like more details or have any other questions? Here are some related questions to explore further:

1. What are the properties of vertical angles?
2. How do linear pairs of angles relate to supplementary angles?
3. What are complementary and supplementary angles?
4. How can we verify the sum of angles around a point?
5. What happens when three or more angles meet at a point?

Tip: Always remember that vertical angles are congruent, and angles forming a straight line sum to 180°.