What is the relationship between 
\[\blueD{\angle m}\] and 
\[\greenD{\angle n}\]?
In a quadrilateral, vertices are labeled clockwise as C, B, A, and D starting from the top-left corner. Angles C B A, B A D, A D C, and D C B are right angles. The midpoint of the line segment B D is labeled by filled point X. Angle C D B is labeled M and angle A D B is labeled N.
\[A\]
\[B\]
\[C\]
\[D\]
\[X\]
\[n\]
\[m\]
Choose 1 answer:
Choose 1 answer:
(Choice A)   Vertical angles
A
Vertical angles
(Choice B)   Complementary angles
B
Complementary angles
(Choice C)   Supplementary angles
C
Supplementary angles
(Choice D)   None of the above
D
None of the above

Let's analyze the given information step by step.

### Given:
- The quadrilateral \(ABCD\) has right angles at each corner, meaning it is a **rectangle**.
- \(X\) is the **midpoint** of segment \(BD\).
- **Angle \(m\) is \(\angle CDB\)**.
- **Angle \(n\) is \(\angle ADB\)**.

### Step 1: Relationship Between \( \angle m \) and \( \angle n \)

Since \(ABCD\) is a rectangle, \(AD\) and \(BC\) are **parallel**, and \(CD\) and \(AB\) are also **parallel**.

- **Angles \( \angle CDB \) (m) and \( \angle ADB \) (n) are on the same straight line \(BD\) (since they share vertex \(D\)).**
- **A pair of angles that form a straight line sum to \(180^\circ\), making them **supplementary angles**.**

Thus, the correct answer is:

**(Choice C) Supplementary angles.**

---

Would you like further clarification or a diagram to visualize the angles?  

Here are five related questions:
1. What are supplementary angles?
2. How do vertical angles differ from supplementary angles?
3. Can two right angles be supplementary?
4. How do we determine if two angles are complementary or supplementary?
5. What is the sum of all interior angles in a quadrilateral?

**Tip:** Supplementary angles always add up to \(180^\circ\), while complementary angles add up to \(90^\circ\).

What is the relationship between \( \angle m \) and \( \angle n \)? In a quadrilateral, vertices are labeled clockwise as C, B, A, and D starting from the top-left corner. Angles C B A, B A D, A D C, and D C B are right angles. The midpoint of the line segment B D is labeled by filled point X. Angle C D B is labeled M and angle A D B is labeled N.

Discover the relationship between angles M (\( \angle CDB \)) and N (\( \angle ADB \)) in a rectangle with right angles at each corner. These angles are supplementary, meaning they add up to 180°. This problem is designed for students in Grades 8-10, covering basic geometric concepts and angle relationships.

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