1. Complementary and
Supplementary Angles

2. These two angles are complementary.
Complementary Angles
Two angles are called complementary angles if the
sum of their degree measurements equals 90 degrees.
Example:
These two angles are complementary.
                                                      
                        

3. These two angles can be "pasted" together to form a right angle!
                        

4. These two angles are supplementary.
Supplementary Angles
Two angles are called supplementary angles if the sum
of their degree measurements equals 180 degrees.
Example:
These two angles are supplementary.
                                                                      

5. These two angles can be "pasted" together to form a straight line!
                                                

6. Complementary and Supplementary
Find the missing angle.
1. Two angles are complementary. One measures 65 degrees.
2. Two angles are supplementary. One measures 140 degrees.
Answer : 25
Answer : 40

7. Complementary and Supplementary
Find the missing angle. You do not have a protractor.
Use the clues in the pictures. 2. 1. x x 55
165
X=35
X=15

8. Interior and Exterior Angles of Triangles

9. Sums of Interior Angles
Triangle
Quadrilateral
Pentagon
= 2 triangles
= 3 triangles
Hexagon
Octagon
= 4 triangles
Heptagon
= 5 triangles
= 6 triangles

10. Convex Polygon
# of Sides
# of Triangles
Sum of Interior Angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
n-gon 3 1
180 4 2
360 5 3
540 6 4
720 7 5
900 8 6
1080 n
n – 2
180•(n – 2)

11. Interior Angles 1 2 3 4 5 6
Exterior Angles

12. Sums of Exterior Angles1 2 3 4 5 6
180
180
180•3 = 540
180
Sum of Interior & Exterior Angles =
540
Sum of Interior Angles =
180
Sum of Exterior Angles =
540- 180=
360

13. Sums of Exterior Angles
Polygon
# of Sides
Interior + Exterior
Interior Angles
Exterior Angles
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
540
180
360
720
360
360
900
540
360
1080
720
360
Sum of Exterior Angles
is always 360!

14. Angles of Regular Polygons
Sum of the Interior Angles
180(n – 2)
Sum of the Exterior Angles
Always 360!
180(n – 2)
Each Interior Angle n
Each Exterior Angle
360 n

15. Parallel Lines And Transversals

16. Transversal
Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
When a transversal t intersects line n and m, eight angles of the following types are formed:
Exterior angles
Interior angles
Consecutive interior angles
Alternative exterior angles
Alternative interior angles
Corresponding angles t m n

17. Vertical Angles & Linear Pair
Two angles that are opposite angles. Vertical angles are congruent.
 1   4,  2   3,  5   8,  6   7
Supplementary angles that form a line (sum = 180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8

18. Angles and Parallel Lines
If two parallel lines are cut by a transversal, then the following pairs of angles are congruent.
Corresponding angles
Alternate interior angles
Alternate exterior angles
If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary.
Consecutive interior angles
Consecutive exterior angles
Continued…..

19. Corresponding Angles & Consecutive Angles
Corresponding Angles: Two angles that occupy corresponding positions.
 2   6,  1   5,  3   7,  4   8 1 2 3 4 5 6 7 8

20. Consecutive Angles
Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.
Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal.
m3 +m5 = 180º, m4 +m6 = 180º 1 2
m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8

21. Alternate Angles  3   6,  4   5  2   7,  1   8 1 2 3 4 5 6
Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair).
Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.
 3   6,  4   5
 2   7,  1   8 1 2 3 4 5 6 7 8

22. Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
m<2=80° m<3=100° m<4=80°
m<5=100° m<6=80° m<7=100° m<8=80°
m<9=100° m<10=80° m<11=100° m<12=80°
m<13=100° m<14=80° m<15=100° m<16=80°

23. If line AB is parallel to line CD and s is parallel to t, find:
Example:
1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.
2. the value of x, if m<1 = 100 and m<8 = 2x + 10.
3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
ANSWERS:
1. 30
2. 35
3. 33