1.6 Angle Pair Relationships

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1.6 Angle Pair Relationships. Geometry Mrs. Spitz Fall 2005. Standards/Objectives:. Standard 3: Students will understand geometric concepts and applications. Objectives: Identify vertical angles and linear pairs. Identify complementary and supplementary angles. Assignment:.

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## 1.6 Angle Pair Relationships

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### 1.6 Angle Pair Relationships

Geometry

Mrs. Spitz

Fall 2005

Standards/Objectives:

Standard 3: Students will understand geometric concepts and applications.

Objectives:

• Identify vertical angles and linear pairs.
• Identify complementary and supplementary angles.
Assignment:
• pp. 47-49 #4-36 all; 41-51 odd

1 &  2,  2 &  3,  3 &  4,

 4&  1

Then what do we call  1 &

 3?

Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays.

 1 &  3,  2 &  4

2

1 3

4

Linear Pair (of angles)
• 2 adjacent angles whose non-common sides are opposite rays.

1 2

Example
• Vertical angles?

1 & 4

1 & 2, 2 & 3,

3 & 4, 4 & 5, 5 & 1

• Linear pair?

5 & 4, 1 & 5

• Adjacent angles not a linear pair?

1 & 2, 2 & 3, 3 & 4

2

1 3

5 4

Important Facts
• Vertical Angles are congruent.
• The sum of the measures of the angles in a linear pair is 180o.
Example:
• If m 5=130o, find

m 3 = 130°

m 6 = 50°

m 4 = 50°

4

5 3

6

A

Example:

E

3x+5o y+20o

B

x+15o 4y-15o

D

• Find x

y

m ABE

m ABD

m DBC

m EBC

C

x=40

y=35

m ABE=125o

m ABD=55o

m DBC=125o

m EBC=55o

Complementary Angles
• 2 angles whose sum is 90o

35o

1

2

55o

A

1 & 2 are complementary

A & B are complementary

B

Supplementary Angles
• 2 angles whose sum is 180o

1 & 2 are supplementary.

X & Y are supplementary.

1 2

130o 50o

X Y

Ex: A & B are supplementary. mA is 5 times mB. Find mA & mB.

mA + mB = 180o

mA = 5(mB)

Now substitute!

5(mB) + mB = 180o

6(mB)=180o

mB=30o

mA=150o