Definition of an acute angle

An acute angle is an angle that measures less than 90° 90° .

Acute angles can appear in triangles, parallelograms, and other geometric shapes where there is an angle less than 90° 90° degrees.

Acute angle

A1- acute angle

Which of the 4 angles presented in the figure corresponds to the description of the acute angle?

what is the definitions of 4 angles

The correct answer is B) 40°

Practice Acute Angles

Examples with solutions for Acute Angles

Exercise #1

ABC ∢\text{ABC} equal to 90°.

What angle is it?

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Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the angle measure provided.
  • Step 2: Match the angle measure to the corresponding type of angle.
  • Step 3: Choose the correct type of angle from the multiple-choice options.

Let's break down the process:

Step 1: The problem specifies that ABC=90\angle \text{ABC} = 90^\circ.

Step 2: Recall the definitions of angle types. A right angle is defined as an angle that measures exactly 90 degrees.

Step 3: Out of the provided choices, select the one that represents a right angle.
- Right angle: =90\angle = 90^\circ (Correct Choice)
- Acute angle: <90\angle < 90^\circ
- Obtuse angle: >90\angle > 90^\circ and <180\angle < 180^\circ
- Flat angle: =180\angle = 180^\circ

Thus, the conclusion is that ABC\angle \text{ABC} is a Right angle.

Answer

Right angle

Exercise #2

What type of angle is

ABC ∢\text{ABC} ?

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Step-by-Step Solution

To determine the type of angle ABC \angle \text{ABC} , we will consider the following:

  • Step 1: Observe the positions of points A, B, and C, which are depicted in the diagram as lying on a straight line.
  • Step 2: Recognize that when three points lie on a straight line and a central point (B here) is between two others (A and C), it forms a flat angle.
  • Step 3: Recall that a flat angle is defined as an angle that measures 180180^\circ, which is the total rotation a line undergoes around a single point.

Visual inspection of the diagram confirms that points A, B, and C create a straight line. Hence, the angle ABC \angle \text{ABC} must be a flat angle.

Therefore, the angle ABC \angle \text{ABC} is a flat angle.

Answer

Flat angle

Exercise #3

ABC ∢\text{ABC} is an angle measuring less than 90°.

What kind of angle angle is it?

AAABBBCCC

Step-by-Step Solution

To determine what kind of angle ABC\angle \text{ABC} is, let's examine the given information: the angle is less than 9090^\circ.

  • Step 1: Recall the types of angles based on their measurements:
    • An acute angle measures less than 9090^\circ.
    • A right angle measures exactly 9090^\circ.
    • An obtuse angle measures greater than 9090^\circ but less than 180180^\circ.
    • A flat angle measures exactly 180180^\circ.
  • Step 2: Match the given information with these definitions.

Since ABC\angle \text{ABC} measures less than 9090^\circ, it fits the definition of an acute angle.

Therefore, the angle ABC\angle \text{ABC} is an acute angle.

Answer

Acute angle

Exercise #4

Which figure depicts a right angle?

Video Solution

Step-by-Step Solution

A right angle is equal to 90 degrees.

In diagrams (a) and (c), we can observe that the angle symbol is a symbol representing an angle that equals 90 degrees.

Answer

Exercise #5

Which of the following angles are obtuse?

Video Solution

Step-by-Step Solution

By definition, an obtuse angle is an angle that is greater than 90 degrees. We can observe that in one drawing there is an angle of 90 degrees and therefore it is not an obtuse angle, the other two angles are less than 90 degrees meaning they are also not obtuse, they are acute angles.

Therefore, none of the answers is correct.

Answer

None of the options

Exercise #6

right angle?

Step-by-Step Solution

To solve this problem, we need to recall the definition of a right angle.

A right angle is defined as an angle that measures exactly 90 90^\circ . This is a standard definition found in geometry, describing an angle formed by the intersection of two perpendicular lines.

Given the multiple-choice options, we need to identify which one corresponds to a right angle:

  • A right angle measures 90 90^\circ .

Let's examine the provided choices:

  1. Angle of 180°.
  2. Minor angle of 90°.
  3. Angle of 90°.
  4. Angle greater than 90°.

Choice 3, "Angle of 90°," directly matches the definition of a right angle.

Therefore, the correct answer is Angle of 90°.

Answer

Angle of 90°.

Exercise #7

What is a flat angle?

Step-by-Step Solution

To solve this problem, let's begin by understanding what a flat angle is:

  • A flat angle is an angle that measures exactly 180180^\circ.
  • Visually, you can think of a flat angle as a straight line, where the two arms of the angle lie on opposite sides of the vertex, forming a straight angle.
  • It is larger than a right angle, which measures 9090^\circ, and exactly twice the measure of a right angle.
  • Flat angles are often used to understand the concept of supplementary angles, where two angles sum up to create a flat angle of 180180^\circ.
  • None of the sides of a flat angle are considered to turn; they continue in a straight direction.

Among the given choices, the option that correctly defines a flat angle is the one that states, "Angle of 180°."

Therefore, the solution to the problem is that a flat angle is an angle of 180180^\circ.

Answer

Angle of 180°.

Exercise #8

True or false?

An acute angle is smaller than a right angle.

Step-by-Step Solution

The definition of an acute angle is an angle that is smaller than 90 degrees.

Since an angle that equals 90 degrees is a right angle, the statement is true.

Answer

True

Exercise #9

True or false?

One of the angles in a rectangle may be an acute angle.

Video Solution

Step-by-Step Solution

One of the properties of a rectangle is that all its angles are right angles.

Therefore, it is not possible for an angle to be acute, that is, less than 90 degrees.

Answer

False

Exercise #10

Choose the appropriate triangle according to the following:

Angle B equals 90 degrees.

Video Solution

Step-by-Step Solution

Let's note in which of the triangles angle B forms a right angle, meaning an angle of 90 degrees.

In answers C+D, we can see that angle B is smaller than 90 degrees.

In answer A, it is equal to 90 degrees.

Answer

AAABBBCCC

Exercise #11

Which figure shows a right angle?

Video Solution

Answer

Exercise #12

Which of the following angles is obtuse?

Video Solution

Answer

Exercise #13

Which of the following angles is straight?

Video Solution

Answer

Exercise #14

Which of the following angles is a plane angle?

Video Solution

Answer

Exercise #15

Which of the angles is not an obtuse angle?

Video Solution

Answer