(7) Lesson 7.2

1. Classify each angle as acute, right, obtuse, or straight.
1. 2.
3.
4. Identify a pair of vertical angles.
5. Tell whether the following statement is true or false. A straight angle
has a measure of 180°.
6. Which of the angles shown in the
diagram at the right are adjacent?
Course 2, Lesson 7-2

2. Course 2, Lesson 7-2
ANSWERS
1. obtuse
2. right
3. acute
4. 1 and 3; 2 and 4
5. True
6. 1 and 2; 2 and 3; 3 and 4; 4 and 1

3. Geometry
Course 2, Lesson 7-2
HOW does geometry help us
describe real-world objects?

4. Course 2, Lesson 7-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
• 7.G.5
Use facts about supplementary, complementary, vertical, and
adjacent angles in a multi-step problem to write and solve simple
equations for an unknown angle in a figure.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.

5. • To identify complementary
and supplementary pairs of
angles
• To use angle relationships to
find missing measures
Course 2, Lesson 7-2
Geometry

6. Course 2, Lesson 7-2
Geometry
• complementary angles
• supplementary angles

7. Course 2, Lesson 7-2
Geometry
symbol
• measure of angle 1 m1

8. Course 2, Lesson 7-2
Geometry
Words Model Symbols
Two angles are complementary if
the sum of their measures is 90˚
m 1 + m 2 = 90  

9. Course 2, Lesson 7-2
Geometry
Words Model Symbols
Two angles are supplementary if
the sum of their measures is 180˚
m 3 + m 4 = 180  

10. 1
Need Another Example?
Step-by-Step Example
1. Identify each pair of angles as complementary,
supplementary, or neither.
∠1 and ∠2 form a straight angle. So, the angles are
supplementary.

11. Answer
Need Another Example?
Identify the pair of angles as complementary,
supplementary, or neither.
supplementary

12. 1
Need Another Example?
Step-by-Step Example
2. Identify each pair of angles as complementary,
supplementary, or neither.
60° + 30° = 90° The angles are complementary.

13. Answer
Need Another Example?
Identify ∠1 and ∠2 as complementary,
supplementary, or neither.
complementary

14. Need Another Example?
Step-by-Step Example
3. Find the value of x.
1
2
3
4
5
Since the two angles form a right
angle, they are complementary.
Words
Variable
Equation
The sum of the measures
of ∠ABC and ∠CBD is 90°
Let 2x represent the measure of ∠CBD.
28 + 2x = 90
28 + 2x = 90 Write the equation.
–28 = –28 Subtract 28 from each side.
So, the value of x is 31.
Divide each side by 2.
x = 31

15. Answer
Need Another Example?
Find the value of x.
62

16. 1
Need Another Example?
2
3
Step-by-Step Example
4. The angles shown are supplementary.
Find the value of x.
123 + 3x = 180 Write the equation.
So, the value of x is 19.
Subtract 123 from each side.–123 = –123
Divide each side by 3.
x = 19

17. Answer
Need Another Example?
The angles shown are complementary.
Find the value of x.
9

18. 1
Need Another Example?
2
3
4
Step-by-Step Example
5. The picture shows a
support brace for a
gate. Find the value
of x.
80 + 10x = 180 Write the equation.
The angle labeled 80° and the angle labeled 10x are
supplementary angles.
Subtract 80 from each side.
Divide each side by 10.
x = 10
ImageSource/Superstock
So, the value of x is 10.
–80 = –80

19. Answer
Need Another Example?
The hour, minute, and second hands make up two
adjacent angles that form a right angle in the clock
shown below. Find the value of x.
3

20. How did what you learned
today help you answer the
Course 2, Lesson 7-2
Geometry
HOW does geometry help us
describe real-world objects?

21. How did what you learned
today help you answer the
Course 2, Lesson 7-2
Geometry
HOW does geometry help us
describe real-world objects?
Sample answers:
• To use complementary and supplementary terms when
describing real-world objects
• To use angle relationships to find missing angle
measures

22. Suppose angles 1 and 2
are complementary. Angle 1
measures 48° and angle 2
measures (3x)°. Write and solve
an equation to find the value of x.
Course 2, Lesson 7-2
Ratios and Proportional RelationshipsFunctionsGeometry