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Which of the following angles are supplementary?

To identify which angles are supplementary in the given diagram, let's examine both sets of intersecting lines:

### Left Diagram:
- The angle labeled \( \angle AMB = 24^\circ \) is given. 
- Since lines \( AN \) and \( BR \) appear to intersect at \( M \), the adjacent angle, \( \angle BMR \), forms a linear pair with \( \angle AMB \). Thus, \( \angle AMB + \angle BMR = 180^\circ \), making these two angles **supplementary**.

- Using this, we can find \( \angle BMR \):
\[
\angle BMR = 180^\circ - 24^\circ = 156^\circ
\]

Therefore, \( \angle AMB = 24^\circ \) and \( \angle BMR = 156^\circ \) are **supplementary**.

### Right Diagram:
- The angle labeled \( \angle PCX = 66^\circ \).
- Lines \( PL \) and \( DX \) intersect at \( C \). The adjacent angle to \( \angle PCX \), which is \( \angle DCL \), forms a linear pair with \( \angle PCX \). So, \( \angle PCX + \angle DCL = 180^\circ \), making these angles **supplementary**.

- Using this, we can find \( \angle DCL \):
\[
\angle DCL = 180^\circ - 66^\circ = 114^\circ
\]

Therefore, \( \angle PCX = 66^\circ \) and \( \angle DCL = 114^\circ \) are **supplementary**.

### Summary:
- \( \angle AMB \) and \( \angle BMR \) are supplementary (24° and 156°).
- \( \angle PCX \) and \( \angle DCL \) are supplementary (66° and 114°).

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:
1. What does it mean for two angles to be supplementary?
2. How do vertical angles relate to supplementary angles in intersecting lines?
3. Can two right angles be supplementary? Why or why not?
4. What is the difference between supplementary and complementary angles?
5. How can we determine if two angles are supplementary without knowing the exact degree?

**Tip:** Supplementary angles always add up to \( 180^\circ \), forming a straight line when placed adjacent to each other.

Learn how to identify supplementary angles in intersecting lines with given angles of 24° and 66°. This problem focuses on the concept of supplementary angles, linear pairs, and angle addition, suitable for students in Grades 7-10.

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