The problem you're showing involves a right triangle. Here's how we can solve for $x$ and $y$:

1. Sum of Angles in a Triangle: The sum of the angles in any triangle is always 180°.

2. Step 1: Find $x$:

   • Since one of the angles is 90° (the right angle), and the other given angle is 38°, we can find $x$ by subtracting these from 180°: $x = 180° - 90° - 38° = 52°$

3. Step 2: Find $y$:

   • Now, looking at the smaller right triangle that has a 67° and 90° angle, we can use the same method to find $y$: $y = 180° - 90° - 67° = 23°$

Final Answer:

• $x = 52°$
• $y = 23°$

Would you like more details on any of the steps?

Here are 5 related questions:

1. How do you calculate the third angle in a triangle when two angles are given?
2. What are the properties of right triangles?
3. How does the Pythagorean theorem apply to right triangles?
4. How can trigonometric ratios (like sine, cosine, and tangent) help find missing sides?
5. How do supplementary and complementary angles relate to triangle problems?

Tip: Always remember that in a triangle, the sum of interior angles is 180°, which can quickly help find missing angles.