1. Angle Relationships

2. Angles
Angles have two sides that share a common endpoint called a vertex of the angle.
Angles are most commonly measured in degrees – for example 90°, 175°
VERTEX
ANGLE
SIDE

3. Classifying Angles – 4 types
RIGHT ANGLE – an angle that is exactly 90°
ACUTE ANGLE – an angle that is less than 90°
OBTUSE ANGLE – an angle that is more than 90°
STRAIGHT ANGLE – an angle that is exactly 180°

4. Naming Angles Sometimes angles use a single letter to name them
Angle H Angle R Angle S

5. Naming Angles
When there are many lines connected with many letters, then you name them by 3 letters.

6. Name the angles

7. Types of Angles Vertical Angles Adjacent Angles Complementary Angles
Supplementary Angles

8. Vertical angles have the same measure.
Angle 1 and 4 are vertical angles 1
ANGLES 2 AND 3 ARE CONGRUENT ANGLES
Angles 2 and 3 are vertical angles 3 2 4
ANGLES 1 AND 4 ARE CONGRUENT ANGLES
When two lines intersect, they form two pairs of opposite angles called VERTICAL ANGLES
Vertical angles have the same measure.
Angles with the same measure are called CONGRUENT ANGLES (equal)

9. The angle labeled x° and the angle labeled 140 are vertical angles.
Find the value of x in the figure x°
140°
140°
The angle labeled x° and the angle labeled 140 are vertical angles.
Therefore, they are congruent.
So, the value of x is 140°

10. Find the value of x in each figure
23° x°
X = 95°
95°

11. ANGLES 1 AND 2 ARE ADJACENT ANGLES3 2 4
When two lines intersect, they form two pairs of side by side angles called ADJACENT ANGLES
Adjacent angles share one vertex and one side

12. Name acute adjacent anglesB C D E F G
Name adjacent angles
Name acute angles
Name acute adjacent angles
Name obtuse angles

13. SUPPLEMENTARY ANGLES
If the sum of 2 angles is 180°, then the angles are SUPPLEMENTARY
120°
60°
145°
35°
120° + 60° = 180°
145° + 35° = 180°

14. COMPLEMENTARY ANGLES
If the sum of 2 angles is 90°, then the angles are COMPLEMENTARY
75°
30°
15°
60°
75° + 15° = 90°
30° + 60° = 90°

15. Classify as complementary, supplementary or neither

16. Complementary, Supplementary or Neither?

17. Finding the value of x in the figure
This angle is 180°
so x = 180
X = 60°
This angle is 90°
So 20 + x = 90
X = 70°

18. Find the value of x in each figure

19. Name complementary angles
Name vertical angles
Name supplementary angles
What is the measure of angle BGC?
What is the measure of angle CGD?

20. Name complementary angles
What is the measure of x?
What is the measure of angle CEA?
What is the measure of angle AED?
Name acute vertical angles
Name obtuse vertical angles
Name supplementary angles