https://file.aiquickdraw.com/mathbot/file/1726996176494bme6hpd8.jpg

The image shows three angles \(x\), \(y\), and \(z\), with one angle labeled as \(47^\circ\), formed by the intersection of two straight lines.

Since these are angles on a straight line, they form supplementary angles and have specific relationships:

1. \( x \) and \( z \) form a linear pair, meaning their sum must be \(180^\circ\). Therefore:
   \[
   x + z = 180^\circ
   \]
   Given that \( z = 47^\circ \), we can calculate \( x \):
   \[
   x + 47^\circ = 180^\circ
   \]
   \[
   x = 180^\circ - 47^\circ = 133^\circ
   \]

2. Angles \( x \) and \( y \) are vertically opposite angles, which means they are equal:
   \[
   y = x = 133^\circ
   \]

Thus, the values of the angles are:
- \( x = 133^\circ \)
- \( y = 133^\circ \)
- \( z = 47^\circ \)

Would you like more details or have any questions?

Here are some related questions:
1. What are vertically opposite angles and why are they equal?
2. How do we calculate supplementary angles?
3. What is a linear pair of angles?
4. What happens to angles when two lines intersect?
5. Can we apply these rules to other geometric shapes?

**Tip:** Always remember that angles formed on a straight line sum up to \(180^\circ\). This rule helps solve many angle problems in geometry.

Solve for the angles x, y, and z in the given diagram where z = 47° and the angles are formed by the intersection of two straight lines.

Learn how to solve for the angles x, y, and z when two straight lines intersect, forming vertically opposite angles and supplementary angles. In this problem, angle z is given as 47°, and the sum of x and z must equal 180°. Suitable for students in Grades 6-8.

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