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In this diagram, we see intersecting lines forming angles. Here's how we can find the missing angles:

1. **Angle \(b\) and the given angle (31°)** are **vertically opposite** angles. Vertically opposite angles are equal. Therefore:
   \[
   b = 31^\circ
   \]

2. **Angle \(c\)** is on a straight line with the 31° angle. Angles on a straight line are **supplementary**, meaning their sum is 180°. Thus, we can calculate angle \(c\) as:
   \[
   c = 180^\circ - 31^\circ = 149^\circ
   \]

Therefore:
- \(b = 31^\circ\)
- \(c = 149^\circ\)

Would you like more details or have any questions?

### Related Questions:
1. What are vertically opposite angles and why are they equal?
2. How do supplementary angles on a straight line add up to 180°?
3. What is the difference between complementary and supplementary angles?
4. How can I identify corresponding and alternate interior angles in a diagram?
5. Are all vertically opposite angles equal regardless of line intersections?

### Tip:
Always remember that vertically opposite angles are equal, and angles on a straight line sum up to 180°.

Find the measure of the missing angles. One angle is given as 31°, and we need to find angles b and c formed by intersecting lines.

Learn how to find the missing angles in a diagram with intersecting lines. Given a 31° angle, discover the measures of the other angles using the vertically opposite angles and supplementary angles theorems. Suitable for Grades 6-8.

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