To solve for the missing angles $x$ and $y$ in this diagram, let's break it down:

1. The given angle is 40° and is adjacent to the angle labeled $x$. These two angles form a straight line, which means they are supplementary. Supplementary angles add up to 180°. $x + 40^\circ = 180^\circ$ Solving for $x$: $x = 180^\circ - 40^\circ = 140^\circ$

2. The angle $y$ is part of a right angle (90°) at the bottom-left corner, and it is vertically opposite to the angle next to $x$, which is also 40°. Vertically opposite angles are equal, so: $y = 40^\circ$

Thus, the missing angles are:

• $x = 140^\circ$
• $y = 40^\circ$

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the relationship between vertically opposite angles?
2. How do complementary and supplementary angles differ?
3. Why do angles on a straight line always sum to 180°?
4. Can angles in different orientations be compared for equality in all cases?
5. How would you solve for angles if the diagram included a triangle?

Tip: Vertically opposite angles are always congruent, no matter the configuration of the lines.