Adjacent Angles and Vertically Opposite Angles

Adjacent Angles and Vertically Opposite Angles

Adjacent Angles

• The word 'adjacent' means 'next to'.

• Two angles are considered 'adjacent' if they are next to each other.

 $\angle ABC$  is equal to 26 degrees.  $\angle CBD\$  is equal to 33 degrees. These two angles are adjacent angles because they are next to each other.

Types of Adjacent Angles

• Complementary Angles - adjacent angles that add to 90 degrees (right angle)

• Supplementary Angles - adjacent angles that add to 180 degrees (straight angle)

• Revolution Angles - adjacent angles that add to 360 degrees (revolution angle)

Complementary Angles

• The complement of 89 degrees is 1 degree, because 89 + 1 = 90

• The complement of 40 degrees is 50 degrees, because 40+50=90

• If one angle is measured to be 35 degrees, the complementary angle can be found by taking 35 degrees away from 90 degrees: 90 - 35 = 55 degrees.

• Note: you can use a calculator for this. If you don't have a calculator, use the calculator on Google.

Multiple Select

Which of the following statements are TRUE? Choose all correct answers. Hint: There are three correct answers.

• Adjacent angles are angles that are next to each other.

• Complementary angles add up to 90 degrees.

• The complement of 80 degrees is 20 degrees.

• If an angle is measured to be 20 degrees, then the complementary angle is 70 degrees.

Multiple Choice

The complement of 85 degrees is...

• 85 degrees

• 5 degrees

• 90 degrees

• none of the above

Multiple Choice

One angle is measured to be 27 degrees. The complementary angle of 27 degrees is... Hint: do 90 - 27 to get your answer.

• 63 degrees

• 90 degrees

• 27 degrees

• 73 degrees

Multiple Choice

One angle is measured to be 71 degrees. The complementary angle of 71 degrees is...

• 71 degrees

• 90 degrees

• 19 degrees

• 61 degrees

Multiple Choice

The image shows a right angle (90 degrees) split into two smaller angles. One angle is 37 degrees. The other angle x is unknown. x and 37 are complementary angles. What is the value of x? Hint: 90 - 37 will give you the answer.

• 63 degrees

• 90 degrees

• 53 degrees

• 37 degrees

Multiple Choice

The image shows a right angle (90 degrees) split into two smaller angles. One angle is 68 degrees. The other angle x is unknown. x and 68 are complementary angles. What is the value of x?

• 90 degrees

• 22 degrees

• 68 degrees

• 32 degrees

Supplementary Angles

• Supplementary angles add to 180 degrees.

• The supplement of 40 degrees is 140 degrees, because 40+140=180

• If one angle is measured to be 170 degrees, the supplementary angle can be found by taking 170 degrees away from 180 degrees: 180 - 170 = 10 degrees.

Multiple Select

Which of the following statements are TRUE? Choose all correct answers. Hint: There are three correct answers.

• The supplement of 120 degrees is 60 degrees.

• Complementary angles add up to 90 degrees.

• Supplementary Angles add up to 180 degrees.

• If an angle is measured to be 20 degrees, then the supplementary angle is 150 degrees.

Multiple Choice

The supplement of 90 degrees is...

• 90 degrees

• 180 degrees

• 0 degrees

• none of the above

Multiple Choice

One angle is measured to be 70 degrees. The supplementary angle of 70 degrees is... Hint: do 180 - 70 to get your answer.

• 110 degrees

• 70 degrees

• 180 degrees

• 90 degrees

Multiple Choice

The image shows a straight angle (180 degrees) split into two smaller angles. One angle is 121 degrees. The other angle ? is unknown. ? and 121 are supplementary angles. What is the value of the ?

• 121 degrees

• 49 degrees

• 59 degrees

• 180 degrees

Revolution Angles

• Revolution angles add to 360 degrees.

• To work out a missing angle, get 360 degrees and subtract out all the other angles around it.

How do I find the ?

Since all of the angles meet at a point, they form a circle (revolution).

To find the ?, you need to get 360 degrees and subtract out 25, 105 and 90. (use a calculator)

? = 360 - 25 - 105 - 90

? = 140 degrees

Multiple Select

Which of the following statements are TRUE? Choose all correct answers. Hint: There are three correct answers.

• Complementary angles add up to 90 degrees.

• Supplementary Angles add up to 180 degrees.

• Revolution angles add up to 360 degrees.

• Supplementary angles add up to 90 degrees.

Multiple Choice

What is the value of the letter 'e' in the diagram?

• $e=214\degree$

• $e=243\degree$

• $e=97\degree$
  

• Hint: takeaway all the other numbers from 360.

Vertically Opposite Angles

Vertically Opposite Angles

• Angles that are formed when two STRAIGHT LINES meet at a point.

• Vertically opposite angles are opposite each other and are EQUAL.

• AOB = DOB = 35 degrees

• AOD = COB = 145 degrees

Multiple Select

Which of the following statements are true?

• Vertically opposite angles are angles that are NEXT to each other.

• Vertically opposite angles are angles that are OPPOSITE to each other.

• Vertically opposite angles are EQUAL.

• Vertically opposite angles are NOT EQUAL.

Multiple Choice

What is the measure (size) of the missing angle in the diagram?

• x = 27 degrees

• x = 127 degrees

• x = 53 degrees

• x = 37 degrees

Multiple Choice

What is the measure (size) of the missing angle in the diagram?

• x = 57 degrees

• x = 33 degrees

• x = 123 degrees

• x = 17 degrees

Classwork

Complete the Quizizz linked on Google Classroom for today's lesson.

Please replay the quiz until you get a score of at least 80%.

If you have any problems or are struggling, you must email me to let me know, so that I can help you.

My email is [e-mail]