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

Step 1: Analyze the given information

• We are provided with an angle of $33^\circ$.
• The angle $y$ is marked as a right angle (90°), which implies it is a perpendicular angle.
• The angle $x$ is formed between the two lines going upwards and rightwards.

Step 2: Using the property of straight lines

• The total angle around a point on a straight line is $360^\circ$.
• The sum of all angles at the point where the lines meet must equal $360^\circ$.

Step 3: Calculate $x$

The angles formed by the lines are complementary (on the same straight line): $x + 33^\circ = 180^\circ \quad \text{(since they form a straight line)}$ $x = 180^\circ - 33^\circ = 147^\circ$

Step 4: Calculate $y$

Since $y$ is a right angle: $y = 90^\circ$

Final Answers:

• $x = 147^\circ$
• $y = 90^\circ$

Would you like further explanation or assistance with other related topics?

Additional Questions:

1. How do we determine the angles in different geometric shapes?
2. What is the sum of interior angles in a triangle?
3. Can we apply these concepts to solve problems with polygons?
4. How do perpendicular lines relate to angles?
5. What is the difference between complementary and supplementary angles?

Tip: Remember that the sum of angles on a straight line is always $180^\circ$, and angles around a point add up to $360^\circ$.