Complementary AnglesTwo angles are called complementary angles if the sum of their degree measurements equals 90 degrees.

Example:

These two angles are complementary.

                                                      

                        

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

                        

Supplementary AnglesTwo angles are called supplementary angles if the sumof their degree measurements equals 180 degrees.

Example:

These two angles are supplementary.

                                                                      

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

                                          

      

Complementary and Supplementary

1. Two angles are complementary. One measures 65 degrees.

2. Two angles are supplementary. One measures 140 degrees.

Find the missing angle.

Answer : 25

Answer : 40

Complementary and Supplementary

Find the missing angle. You do not have a protractor.Use the clues in the pictures.

1.2.x

55 165x

X=35 X=15

Interior and Exterior Angles of Triangles

SUMS OF INTERIOR ANGLES

Triangle Quadrilateral Pentagon

Heptagon OctagonHexagon

= 2 triangles = 3 triangles

= 4 triangles= 5 triangles = 6 triangles

Convex Polygon

# of Sides # of Triangles

Sum of Interior Angles

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

n-gon

3

4

5

6

7

8

n

1

2

3

4

5

6

n – 2

180360

540

720

900

1080

180•(n – 2)

12

34

5 6

Exterior Angles

Interior Angles

Sum of Interior Angles =

Sum of Interior & Exterior Angles =

180

12

34

5 6

180

180

180

540

Sum of Exterior Angles = 360 540- 180=

SUMS OF EXTERIOR ANGLES

180•3 = 540

SUMS OF EXTERIOR ANGLES

Polygon # of Sides

Interior +

Exterior

Interior Angles

Exterior Angles

Triangle 3

Quadrilateral 4

Pentagon 5

Hexagon 6

180

360

540

720

540

720

900

1080

360

360

360

360Sum of Exterior Angles

is always 360!

ANGLES OF REGULAR POLYGONS

Sum of the Interior Angles

Sum of the Exterior Angles

Each Interior Anglen

Each Exterior Angle n

180(n – 2)

Always 360!

180(n – 2)

360

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 anglesInterior anglesConsecutive interior anglesAlternative exterior anglesAlternative interior anglesCorresponding angles

tm

n

17

Vertical Angles & Linear Pair

Vertical Angles:

Linear Pair:

1 4, 2 3, 5 8, 6 7

Two angles that are opposite angles. Vertical angles are congruent.

1 & 2 , 2 & 4 , 4 &3, 3 & 1,

5 & 6, 6 & 8, 8 & 7, 7 & 5

Supplementary angles that form a line (sum = 180)

1 23 4

5 67 8

18

Angles and Parallel Lines

• If two parallel lines are cut by a transversal, then the following pairs of angles are congruent.

1. Corresponding angles

2. Alternate interior angles

3. Alternate exterior angles

• If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary.

1. Consecutive interior angles

2. 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 23 4

5 67 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.

m3 +m5 = 180º, m4 +m6 = 180º

m1 +m7 = 180º, m2 +m8 = 180º

1 23 4

5 67 8

21

Alternate Angles

• 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 81 2

3 4

5 67 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.

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°

t

16 15

1413

12 11

109

8 7

65

34

21

s

DC

BA

23

Example:

1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.

If line AB is parallel to line CD and s is parallel to t, find:

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.

ANSWERS:

t

16 151413

12 11109

8 7

65

34

21

s

DC

BA

1. 30

2. 35

3. 33