Solve Problems Using Angle Relationships

Lesson Goals are to be able to:

find the measure of angle using angle relationships
recognize the relationship between different angles fromed by lines and rays

Angles are made up of two sides, that can be formed by line segments or rays. The point where the two join together is called the vertex.

Angles are called using three letters or a number.

There are three main types of angles:

acute angles are less than 90º
obtuse angles are between greater than 90º, but less than 180º
right angles are equal to 90º

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Plus we have four basic angle relationships

Complementary angles add up to equal 90º
Supplementary angles add up to equal 180º
Adjacent angles share a common ray or line segment, because they are next to each other
Vertical angles are formed by two intersecting lines

An angle relationship is formed between two angles.

Practice

Examine the image. Use clues from the image as well as your angle types and relationships to answer each question.

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2

Match each pair of angles to the angle relationship they show.

Item 2
Item 1

complementary angles
supplementary angles

1

All of the angle pairs in question one are examples of

vertical angles

acute angles

obtuse angles

adjacent angles

2

Name a pair of vertical angles.

Solving Problems Based on Angle Relationships

Watch each video to learn how to utilize the four types of angle relationships to solve for x and determine any missing angle measures. Complete the practice problem after each video to test your knowledge.

2

Solve for the value of x.

2

Calculate the measure of the bigger angle.

2

Calculate the measure of the acute angle.

1

Find the value of x.

42º

180º

126º

54º

1

Find the value of x.

4

8

6

2

1

Determine the value of the smaller angle.

1

Determine the value of the larger angle.

75º

64º

89ª

100º

1

Find the value of x.

72.5º

145º

65º

130º

1

Find the value of x.

40º

140º

240º

120º

Test Yourself

Put all your knowledge on angles together to solve each problem.

3

1

Calculate the value of each angle.

a = 35º and b = 80º

a = 90º and b = 35º

a = 80º and b = 35º

Not enough information has been given to determine the value of each angle.

a = 35º and b = 90º

3

Determine the value of the angle represented by the "?" in the image.

4

Angles

Solve Problems Using Angle Relationships

Solving Problems Based on Angle Relationships

Test Yourself

Angles

Solve Problems Using Angle Relationships

Practice

Match each pair of angles to the angle relationship they show.

All of the angle pairs in question one are examples of

Name a pair of vertical angles.

Solving Problems Based on Angle Relationships

Solve for the value of x.

Calculate the measure of the bigger angle.

Calculate the measure of the acute angle.

Find the value of x.

Find the value of x.

Determine the value of the smaller angle.

Determine the value of the larger angle.

Find the value of x.

Find the value of x.

Test Yourself

Calculate the value of each angle.

Determine the value of the angle represented by the "?" in the image.

Calculate the measure of all missing angles.

Practice

Match each pair of angles to the angle relationship they show.

All of the angle pairs in question one are examples of

Name a pair of vertical angles.

Solve for the value of x.

Calculate the measure of the bigger angle.

Calculate the measure of the acute angle.

Find the value of x.

Find the value of x.

Determine the value of the smaller angle.

Determine the value of the larger angle.

Find the value of x.

Find the value of x.

Calculate the value of each angle.

Determine the value of the angle represented by the "?" in the image.

Calculate the measure of all missing angles.