1.5 complementary and supplementary angles

WARM UP 1/22/13Mark no school on 1/20/13.

Identify the type of angle:

1.30°8. 60 °

2.120 ° 9. 158 °

3.180 ° 10. 80 °

4.90 °

5.72 °

6.140 °

7.116 °

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

Example:

These two angles are complementary. WHY????

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. WHY???

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

Vertical AnglesPairs of Angle formed by the intersection of 2 lines.They are across from each other.

How many pairs?

                             Vertical angles are congruent!!!

Review

State whether the following are acute, right, or obtuse.1.

2.

3.

4.

5.

??

acute obtuseright

obtuseacute

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

Vertical Angles

Find the missing angle. You do not have a protractor.

Use the clues in the pictures.

58x

X=58

Identify Complements and Supplements

• Determine whether the angles are complementary, supplementary, or neither.

a.

a. Because 22° + 158° = 180°, the angles are supplementary.

22° 158°

• Determine whether the angles are complementary, supplementary, or neither.

b.

b. Because 15° + 85° = 100°, the angles are neither complementary or supplementary.

15° 85°

• Determine whether the angles are complementary, supplementary, or neither.

c.

c. Because 55° + 35° = 90°, the angles are complementary.

35°55°

Example Identify Complements and Supplements

Determine whether the angles are complementary, supplementary, or neither.

a. b. c.

SOLUTION

a. Because 22° + 158° = 180°, the angles are supplementary.

b. Because 15° + 85° = 100°, the angles are neither complementary nor supplementary.

c. Because 55° + 35° = 90°, the angles are complementary.

Checkpoint Identify Complements and Supplements

ANSWER supplementary

ANSWER complementary

Determine whether the angles are complementary, supplementary, or neither.

1. ANSWER neither

2.

3.

• Tell whether the numbered angles are adjacent or nonadjacent.

a.

a. Because the angles do not share a common vertex or a common side, then

and are nonadjacent.

1

2

21

• Tell whether the numbered angles are adjacent or nonadjacent.

b.

Because the angles share a common vertex and a common side, and they do not have an common interior points, and

are adjacent.

3 4

43

• Tell whether the numbered angles are adjacent or nonadjacent.

c.

Although and share a common vertex, they do not share a common side. Therefore, andare nonadjacent.

5

6

655 6

Example Measures of Complements and Supplements

A is a complement of C, and mA = 47°. Find mC.a.

b. P is a supplement of R, and mR = 36°. Find mP.

SOLUTION

a. A and C are complements, so their sum is 90°.

b.P and R are supplements, so their sum is 180°.

mA + mC = 90° mP + mR = 180°

47° + mC = 90° mP + 36° = 180°

47°+ mC – 47° = 90° – 47° mP + 36° – 36° = 180° – 36°

mC = 43° mP = 144°

Checkpoint Measures of Complements and Supplements

B is a complement of D, and mD = 79°. Find mB.4.

5. G is a supplement of H, and mG = 115°. Find mH.

ANSWER 11°

ANSWER 65°

Congruent Complements Theorem

1 12 3

Congruent Supplements Theorem

1 12 3

SOLUTION

7 and 9 are both supplementary to 8. So, by the Congruent supplements Theorem, 7 9.

7 and 8 are supplementary, and 8 and 9 are supplementary. Name a pair of congruent angles. Explain your reasoning.

ANSWER10 12; 10 and 12 are both complementary to 11, so 10 12 by the Congruent Complements Theorem.

In the diagram, m10 + m11 = 90°, and m11 + m12 = 90°.

Name a pair of congruent angles. Explain your reasoning.

More drawings

20

C

J

D

E F

G

H

70

9070

20

90

I

Final Drawing

52

B

A

F E

D

C

60

G

68

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