https://file.aiquickdraw.com/mathbot/file/1726176416120zrwtl23j.jpg

Let's go through the problem to figure out why the answers might be incorrect.

### Given:
- You need to find the values of the unknown angles \( x^\circ \), \( y^\circ \), and \( z^\circ \).
- One angle is already given as \( 72^\circ \).
- There is a right angle marked at the intersection of two lines, indicating \( 90^\circ \).

### Analyzing the diagram:
1. **Angle \( x^\circ \)** is vertically opposite to the \( 72^\circ \) angle, and vertically opposite angles are equal. Therefore:
   \[
   x = 72^\circ
   \]
   
2. **Angle \( z^\circ \)** forms a linear pair with the \( 72^\circ \) angle, meaning \( z^\circ + 72^\circ = 180^\circ \) (since angles on a straight line sum up to 180°). So:
   \[
   z = 180^\circ - 72^\circ = 108^\circ
   \]

3. **Angle \( y^\circ \)** is part of the right-angled corner, where angles form a right angle. This means \( y^\circ + 72^\circ = 90^\circ \), so:
   \[
   y = 90^\circ - 72^\circ = 18^\circ
   \]

The answers you have written as \( x = 72^\circ \), \( y = 18^\circ \), and \( z = 108^\circ \) are **correct** based on the geometric principles involved in the problem.

It seems the error might be unrelated to the values themselves. Could there have been an issue with input formatting or the way the answer was submitted? You may want to verify this with the instructions provided in your worksheet or platform.

Would you like further details on how these angle relationships work?

### Here are 5 related questions to expand your understanding:
1. What are vertically opposite angles and how are they calculated?
2. What is the definition of a linear pair of angles?
3. How do angles around a point add up, and why is that always the case?
4. Can complementary and supplementary angles be used in non-right-angle scenarios?
5. How can transversal lines help in determining angle relations?

### Tip:
When solving angle problems, always look for relationships such as vertical angles, linear pairs, and complementary or supplementary angles. These clues often simplify the process.

Find the value of the unknown angles. x = ?, y = ?, z = ?, with given angle 72° and a right angle marked at the intersection of two lines.

This geometry problem involves finding the unknown angles x, y, and z based on the given angle of 72° and a right angle. Concepts covered include vertically opposite angles, linear pairs, and complementary angles. Suitable for students in Grades 7-8.

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