Types of Angles - Examples, Exercises and Solutions

Understanding Types of Angles

Complete explanation with examples

What is an angle?

Definition: Angles are created at the intersection between two lines. As seen in the following illustration

Angles are created at the intersection between two lines

The angle in the illustration is called AB AB . We could also call it angle ABC \sphericalangle ABC . The important thing is that the middle letter is the one at the intersection of the lines.

For example, in this case:

We could also call it angle ABC

The angle is BCD \sphericalangle BCD or DCB \sphericalangle DCB . Both notations are correct for the same angle.

We usually mark the angle with an arc as follows:

The angle is BCD

The marked angle is ABC ∡ABC . Sometimes we will denote angles using Greek letters, for example:

α α or β β

Before the name of the angle, we should note the angle symbol, like this:

Together it looks like this:

CBA ∡CBA or α ∡α

Next, we will delve into the size of angles, the different types, and those that are created when a line intersects two parallel lines.

Detailed explanation

Practice Types of Angles

Test your knowledge with 27 quizzes

Find the size of angle \( \alpha \).

27.727.727.7AAABBBCCC41

Examples with solutions for Types of Angles

Step-by-step solutions included
Exercise #1

What type of angle is α \alpha ?

αα

Step-by-Step Solution

Remember that an acute angle is smaller than 90 degrees, an obtuse angle is larger than 90 degrees, and a straight angle equals 180 degrees.

Since the lines are perpendicular to each other, the marked angles are right angles each equal to 90 degrees.

Answer:

Straight

Exercise #2

What is the size of the missing angle?

80

Step-by-Step Solution

To find the size of the missing angle, we will use the property that the sum of angles on a straight line is 180180^\circ. Given that one angle is 8080^\circ, we can calculate the missing angle using the following steps:

  • Step 1: Recognize that the given angle α=80\alpha = 80^\circ and the missing angle β\beta form a straight line.
  • Step 2: Use the angle sum property for a straight line: α+β=180 \alpha + \beta = 180^\circ
  • Step 3: Substitute the known value: 80+β=180 80^\circ + \beta = 180^\circ
  • Step 4: Solve for the missing angle β\beta: β=18080=100 \beta = 180^\circ - 80^\circ = 100^\circ

Therefore, the size of the missing angle is 100100^\circ.

Answer:

100°

Video Solution
Exercise #3

Indicates which angle is greater

Step-by-Step Solution

Note that in drawing B, the two lines form a right angle, which is an angle of 90 degrees:

While the angle in drawing A is greater than 90 degrees:

Therefore, the angle in drawing A is larger.

Answer:

Video Solution
Exercise #4

Indicates which angle is greater

Step-by-Step Solution

Answer B is correct because the more closed the angle is, the more acute it is (less than 90 degrees), meaning it's smaller.

The more open the angle is, the more obtuse it is (greater than 90 degrees), meaning it's larger.

Answer:

Video Solution
Exercise #5

Which angle is greater?

Step-by-Step Solution

The angle in diagram (a) is more acute, meaning it is smaller:

Conversely, the angle in diagram (b) is more obtuse, making it larger.

Answer:

Video Solution

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