Question

What is the measure of________ 1. 22 degrees 2. 56 degrees 3. 89 degrees 4. 112 degrees

Answer 1

The measure of:

1.
`\(22^\circ\)` is an acute angle.

2.
`\(56^\circ\)` is an acute angle.

3.
`\(89^\circ\)` is an acute angle.

4.
`\(112^\circ\)` is an obtuse angle.

Step-by-step explanation:

In geometry, angles are classified based on their measures. An acute angle is one that measures less than
`\(90^\circ\)`, while an obtuse angle measures more than
`\(90^\circ\)`.

For the given angles:

1.
`\(22^\circ\)` is less than
`\(90^\circ\),` so it is an acute angle.

2.
`\(56^\circ\)` is also less than
`\(90^\circ\),`, indicating it is an acute angle.

3.
`\(89^\circ\)` falls just below the right angle measure, making it an acute angle.

4.
`\(112^\circ\)` is greater than
`\(90^\circ\),`, classifying it as an obtuse angle.

These classifications are based on the fundamental properties of angles, where a right angle measures exactly
`\(90^\circ\),`. When an angle is smaller than a right angle, it is acute, and when it is larger, it is obtuse.

Understanding these angle classifications is essential in geometry and various real-world applications, such as in engineering, architecture, and physics. Acute angles are often encountered in triangles, while obtuse angles play a significant role in the study of shapes and spatial relationships.

Answer 2

The measures of the given angles are as follows:

1.
`\(22^\circ\)`

2.
`\(56^\circ\)`

3.
`\(89^\circ\)`

4.
`\(112^\circ\)`

Step-by-step explanation:

In geometry, the measure of an angle is the amount of rotation needed to bring one line or plane into coincidence with another. Angles are typically measured in degrees, a unit of angular measure.

1.
`\(22^\circ\):`

The measure of
`\(22^\circ\)`indicates a relatively small angle. To understand its significance, consider a full circle, which is
`\(360^\circ\)`.
`\(22^\circ\)` represents a fraction of this circle, showing a moderate rotation.

2.
`\(56^\circ\):`

`\(56^\circ\)`is larger than
`\(22^\circ\)`, signifying a more substantial rotation. To put it in perspective,
`\(56^\circ\)` is approximately one-sixth of a full circle, offering a clearer sense of the extent of the angular displacement.

3.
`\(89^\circ\):`

`\(89^\circ\)`is very close to
`\(90^\circ\)`, which is a right angle. This angle is just shy of forming a right angle, emphasizing its proximity to a perpendicular orientation. Understanding this angle aids in visualizing geometric relationships.

4.
`\(112^\circ\):`

`\(112^\circ\)` is greater than
`\(90^\circ\)`, indicating an obtuse angle. Visualizing
`\(112^\circ\)` helps to recognize its deviation from a right angle and reinforces the concept of obtuse angles in geometry.