Types of Angles Practice Problems - Right, Acute, Obtuse

Master angle classification with interactive practice problems. Learn to identify right, acute, obtuse, and straight angles through guided examples and solutions.

📚What You'll Practice with Angle Types
  • Identify acute angles measuring less than 90 degrees
  • Recognize right angles that measure exactly 90 degrees
  • Classify obtuse angles measuring between 90 and 180 degrees
  • Distinguish straight angles that measure exactly 180 degrees
  • Apply angle classification to triangles and polygons
  • Solve problems involving angle measurements and comparisons

Understanding Acute Angles

Complete explanation with examples

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°

Detailed explanation

Practice Acute Angles

Test your knowledge with 6 quizzes

The triangle ABC is a right triangle.

Which angle is larger, \( ∢B \) or \( ∢A \)?

AAABBBCCC

Examples with solutions for Acute Angles

Step-by-step solutions included
Exercise #1

Which figure depicts a right angle?

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:

Video Solution
Exercise #2

Which of the following angles are obtuse?

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

Video Solution
Exercise #3

What type of angle is

ABC ∢\text{ABC} ?

AAABBBCCC

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 #4

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 #5

ABC ∢\text{ABC} equal to 90°.

What angle is it?

AAABBBCCC

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

Frequently Asked Questions

What is the difference between acute and obtuse angles?

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An acute angle measures less than 90°, while an obtuse angle measures between 90° and 180°. Acute angles are 'sharp' and narrow, whereas obtuse angles are 'wide' and open.

How do you identify a right angle without a protractor?

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A right angle forms a perfect square corner, like the corner of a book or paper. It measures exactly 90° and is often marked with a small square symbol in geometric diagrams.

What are the 4 main types of angles by measurement?

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The four main types are: 1) Acute angles (less than 90°), 2) Right angles (exactly 90°), 3) Obtuse angles (90° to 180°), and 4) Straight angles (exactly 180°).

Can a triangle have more than one obtuse angle?

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No, a triangle cannot have more than one obtuse angle. Since the sum of angles in a triangle is 180°, having two obtuse angles would exceed this limit.

What angle measures exactly 180 degrees?

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A straight angle measures exactly 180°. It forms a straight line and appears as if the two rays are pointing in opposite directions from the vertex.

How are angles measured in geometry?

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Angles are typically measured in degrees (°) using a protractor. The measurement represents the amount of rotation from one ray to another around the vertex point.

What is an example of an acute angle in real life?

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Common examples of acute angles include the tip of a pencil, the hands of a clock at 1:00, or the peak of a roof. Any angle smaller than a right angle corner is acute.

Why is it important to learn angle types?

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Understanding angle types is fundamental for geometry, trigonometry, and real-world applications like construction, engineering, and art. It helps in solving problems involving shapes, rotations, and spatial relationships.

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