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°.