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In the given problem, we are looking at a diagram and question based on angles and geometry. Here's a clear transcription of the question:

**Question:**
In the diagram below, ∠XZY is a right angle. If ∠XZW = 43°, and ZW is shown to be on the same straight line as ZY, find ∠WZY.

**Solution Approach:**

1. **Recognize the straight angle:**
   Since ∠XZY is a right angle (90°) and ZW is on the same straight line as ZY, this implies that the total angle on a straight line is 180°.

2. **Use the given angles:**
   ∠XZW = 43°, and since ZW and ZY form a straight line, the sum of the angles around point Z on this straight line must be 180°. Therefore, we can calculate ∠WZY as follows:
   \[
   ∠XZW + ∠WZY = 180°
   \]
   \[
   43° + ∠WZY = 180°
   \]
   \[
   ∠WZY = 180° - 43° = 137°
   \]

Thus, the measure of ∠WZY is **137°**.

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Would you like further details or any clarification on this solution? Here are 5 related questions for additional practice:

1. If ∠XZW was 50°, what would ∠WZY be?
2. In a triangle with one right angle, what is the sum of the other two angles?
3. Can you explain why the sum of the angles on a straight line is always 180°?
4. How can you use the properties of supplementary angles to solve geometric problems?
5. What is the difference between complementary and supplementary angles?

**Tip:** When working with angles, always consider the properties of straight lines, triangles, and the relationships between adjacent angles to simplify complex problems.

In the diagram below, ∠XZY is a right angle. If ∠XZW = 43°, and ZW is shown to be on the same straight line as ZY, find ∠WZY.

Learn how to solve a geometry problem involving a right angle and a straight line, where you are required to find an unknown angle using the supplementary angles theorem. Suitable for students in Grades 7-9.

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