1. 7-3 Angle Relationships Warm Up Problem of the Day Lesson Presentation
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. 7-3 Angle Relationships Problem of the Day
Course 1
7-3
Angle Relationships
Problem of the Day
A line forms an angle of 57° with the vertical axis. What angle does the line form with the horizontal axis?
33° or 147°

3. Learn to understand relationships of angles.
Angle Rationships!

4. Warm Up
Identify the type of angle.
1. 75°
2. 90°
3. 91°
4. 180°
acute
right
obtuse
straight

5. MORE WARM-UP
1. How do you name a ray?
Under the ray
symbol, name first the endpoint and then
any other point on the ray.
2. What is the measure of an obtuse angle?
between 90° and 180°
3. How do you name a line?
Under the line symbol, name any two
points on a line.
4. What is the measure of an acute angle?
Between 1° and 89 °.

6. Insert Lesson Title Here
Vocabulary
congruent
vertical angles
adjacent angles
complementary angles
supplementary angles

7. MRP and NRQ are vertical angles. MRN and PRQ are vertical angles
When angles have the same measure, they are said to be congruent. – same size and shape! M N
160°
20° R P Q
Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent.
MRP and NRQ are vertical angles.
MRN and PRQ are vertical angles

8. MRN and NRQ are adjacent angles. They share vertex R and RN.
Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent. M N
160°
20° R P Q
MRN and NRQ are adjacent angles. They share vertex R and RN.
NRQ and QRP are adjacent angles. They share vertex R and RQ.

9. Additional Example 1A: Identifying Types of Angle Pairs
Identify the type of each angle pair shown. A.
5 and 6 are opposite each other and are formed by two intersecting lines.
They are vertical angles.

10. Additional Example 1B: Identifying Types of Angle Pairs
Identify the type of each angle pair shown. B.
7 and 8 are side by side and have a common vertex and ray.
7 8
They are adjacent angles.

11. Try This: Additional Example 1A
Identify the type of each angle pair shown. A.
3 and 4 are side by side and have a common vertex and ray. 3 4
They are adjacent angles.

12. Try This: Additional Example 1B
Identify the type of each angle pair shown. B. 7 8
7 and 8 are opposite each other and are formed by two intersecting lines.
They are vertical angles.

13. Complementary angles are two angles whose measures have a sum of 90°.
65° + 25° = 90°
LMN and NMP are complementary. P N M L
25°
65°

14. Supplementary angles are two angles whose measures have a sum of 180°.
65° + 115° = 180°
GHK and KHJ are supplementary. J K H
115°
65° G

15. Additional Example 2A: Identifying an Unknown Angle Measure
Find each unknown angle measure.
A. The angles are complementary.
The sum of the measures is 90°.
71° + a = 90° a
–71° –71°
a = 19°
71°

16. Additional Example 2B: Identifying an Unknown Angle Measure
Find each unknown angle measure.
B. The angles are supplementary.
125° + b = 180°
The sum of the measures is 180°.
–125° –125°
b = °
125° b

17. Additional Example 2C: Identifying an Unknown Angle Measure
Find each unknown angle measure.
C. The angles are vertical angles. c
82°
c = 82°
Vertical angles are congruent.

18. Additional Example 2D: Identifying an Unknown Angle Measure
Find each unknown angle measure. x
80° K M L N J y
D. JKL and MKN are congruent.
x + y + 80° = 180°
The sum of the measures is 180°.
–80° –80°
x + y = 100°
Each angle measures half of 100°.
x = 50° and y = 50°

19. Find each unknown angle measure.
Try This: Example 2A
Find each unknown angle measure.
A. The angles are complementary.
65° + d = 90°
The sum of the measures is 90°. d
–65° –65°
d = 25°
65°

20. Try This: Example 2B
Find each unknown angle measure.
B. The angles are supplementary.
145° + s = 180°
The sum of the measures is 180°.
–145° –145°
s = °
145° s

21. Find each unknown angle measure.
Try This: Example 2C
Find each unknown angle measure.
C. The angles are vertical angles. t
t = 32°
Vertical angles are congruent.
32°

22. Try This: Example 2D
Find each unknown angle measure. x
50° B D C E A y
D. ABC and DBE are congruent.
x + y + 50° = 180°
The sum of the measures is 180°.
–50° –50°
x + y = 130°
Each angle measures half of 130°.
x = 65° and y = 65°

23. Insert Lesson Title Here
Lesson Quiz
Give the complement of each angle.
1. 70° °
Give the supplement of each angle.
3. 120° °
5. Identify the type of angle pair shown.
20°
48°
60°
163°
adjacent