Solving Angle Relationships

Angle Relationships

​How to find missing angles using angle properties

​Complimentary Angles

Complimentary angles are two angles that have a sum of 90 degrees​.

Multiple Choice

If the two angles shown are complimentary angles, what would be the measure of angle x?

• 53 degrees

• 90 degrees

• 37 degrees

• 73 degrees

Multiple Choice

If the two angles shown are complimentary angles, what would be the measure of angle x?

• 90 degrees

• 20 degrees

• 15 degrees

• 75 degrees

​Supplementary Angles

​Supplementary angles are angles that have a sum of 180 degrees.

Multiple Choice

If the two angles shown are supplementary angles, what would be the measure of angle x?

• 52 degrees

• 76 degrees

• 118 degrees

• 62 degrees

Multiple Choice

If the three angles shown are supplementary angles, what would be the measure of angle x?

• 86 degrees

• 79 degrees

• 21 degrees

• 48 degrees

​Vertical Angles

​Vertical angles are angles that are opposite of each other when two lines intersect. Vertical angles are congruent (equal) to each other.​

Multiple Select

Which pairs of angles are vertical angles? Check all that apply.

• The 76 degree angle and angle y are vertical angles

• Angles y and z are vertical angles

• Angles x and z are vertical angles

• The 76 degree angle and angle z are vertical angles

Multiple Choice

What is the measure of angle x?

• 130 degrees

• 50 degrees

• 90 degrees

• 40 degrees

​Angle Theorems

​1) Traingle Sum Theorem- The three angles INSIDE a triangle add to 180 degrees

2) The Exterior Angle Theorem- the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Example of Triangle Sum Theorem

​Recall: Interior angles in a triangle add to 180 degrees

Find the measurement of the missing angle in the picture shown:

68 + 47 = 115
180 - 115 = 65 degrees

Example of Exterior angle theorem

​Recall: an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Find the measurement of the missing angle in the picture shown:

60 + 70 = 130 degrees

Multiple Choice

What is the measure of angle x? Use the Exterior Angle Theorem to solve the problem.

• Angle x has a measure of 109 degrees

• Angle x has a measure of 64 degrees

• Angle x has a measure of 45 degrees

• Angle x has a measure of 19 degrees

Multiple Choice

What is the measure of angle x? Use the Exterior Angle Theorem to solve the problem.

• Angle x has a measure of 144 degrees

• Angle x has a measure of 39 degrees

• Angle x has a measure of 111 degrees

• Angle x has a measure of 75 degrees

​Let's try some mixed practice. Use what you have learned in the previous slides to solve this next set of problems.

Fill in the Blanks

Fill in the Blanks

Multiple Choice

Choose the correct measurements for the missing angles in the diagram

• angle x = 104

  angle y = 104

  angle z = 104

• angle x = 104

  angle y = 76

  angle z = 104

• angle x = 76

  angle y = 104

  angle z = 76

• angle x = 104

  angle y = 76

  angle z = 76

Multiple Choice

What is the measure of angle x?

• 35 degrees

• 10 degrees

• 80 degrees

• 65 degrees

Multiple Choice

If the angle marked in orange is 118 degrees and the angle marked in red is 90 degrees, what would be the measure of angle f?

• 28 degrees

• 118 degrees

• 35 degrees

• 62 degrees

Here is a summary of the angle relationships we have learned about in this lesson. You are finished!