
3. What is the complementary angle of 45°? Can one of the complementary angles be
obtuse? Justify.


### Complementary Angle of 45°

**Complementary angles** are two angles whose measures add up to \(90^\circ\).

Given the angle \(45^\circ\), the complementary angle can be found using the equation:

\[
90^\circ - 45^\circ = 45^\circ
\]

Thus, the complementary angle of \(45^\circ\) is also \(45^\circ\).

### Can One of the Complementary Angles Be Obtuse?

No, one of the complementary angles cannot be obtuse. Here's why:

- **Obtuse Angle Definition**: An obtuse angle is any angle that measures greater than \(90^\circ\).

- **Complementary Angles Definition**: By definition, complementary angles sum to \(90^\circ\).

If one of the angles were obtuse (greater than \(90^\circ\)), the sum of the two angles would exceed \(90^\circ\), which contradicts the definition of complementary angles. Therefore, it is impossible for one of the complementary angles to be obtuse. All complementary angles must be acute (less than \(90^\circ\)) to satisfy the condition that their sum is \(90^\circ\).

If you have any questions or want further details, feel free to ask! Here are some related questions:

1. What are supplementary angles, and how do they differ from complementary angles?
2. Can two acute angles ever form a supplementary pair? Why or why not?
3. How can you find the complementary angle for a given angle using a protractor?
4. What are the properties of complementary angles in a right triangle?
5. Can complementary angles be equal in measure?
6. How do complementary angles relate to the angles in a right triangle?
7. What is the sum of two complementary angles and two supplementary angles?
8. Can an angle be complementary to itself? If so, what is its measure?

### Tip

To quickly check if two angles are complementary, simply add them. If their sum is exactly \(90^\circ\), they are complementary.

Explore the concept of complementary angles and solve for the complementary angle of 45°. This problem delves into basic geometry, specifically angles and their relationships, explaining why one of the complementary angles cannot be obtuse. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation