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1.5 –Describe Angle Pair Relationships PowerPoint Presentation

1.5 –Describe Angle Pair Relationships

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1.5 –Describe Angle Pair Relationships

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1.5 –Describe Angle Pair Relationships

Adjacent angles:

Two angles that share a common side and vertex

2

1

1 is adjacent to 2

Complementary Angles:

Two angles that add to 90°

1

2

1

2

m1 + m2 = 90°

Supplementary Angles:

Two angles that add to 180°

2

1

1

m1 + m2 = 180°

2

Two adjacent angles whose noncommon sides are opposite rays

Linear Pair:

2

1

They will always add to 180°

m1 + m2 = 180°

Vertical Angles:

Two angles whose sides form two pairs of opposite rays

1

2

They will always be congruent!

1. Tell whether the indicated angles are adjacent.

EFG and HGF

no

1. Tell whether the indicated angles are adjacent.

JNM and MNK

yes

2. Name a pair of complementary angles, supplementary angles, and vertical angles .

Vertical:

ROL and NOP

L

LOM and QOP

M

Complementary:

R

N

QOR and ROL

O

MON and NOP

Q

P

Supplementary:

ROL and LON

ROM and MON

QOL and LOM

2. Name a pair of complementary angles, supplementary angles, and vertical angles .

Vertical:

DGE and BGC

A

EGB and DGC

E

Complementary:

DGE and EGA

G

B

D

Supplementary:

C

DGE and EGB

DGA and AGB

EGA and AGC

3. 1 and 2 are complementary angles. Given the measure of 1, find m2.

m1 = 82°

m2 =

90 – 82 =

8°

3. 1 and 2 are complementary angles. Given the measure of 1, find m2.

m1 = 23°

m2 =

90 – 23 =

67°

4. 1 and 2 are supplementary angles. Given the measure of 1, find m2.

m1 = 82°

m2 =

180 – 82 =

98°

4. 1 and 2 are supplementary angles. Given the measure of 1, find m2.

m1 = 105°

m2 =

180 – 105 =

75°

5. Find the measure of ABD and DBC.

4x + 6 + 11x – 6 = 180

15x = 180

x = 12

4(12)+6

mABD =

= 48+6

= 54°

11(12)-6

mDBC =

= 132-6

= 126°

5. Find the measure of ABD and DBC.

2x + 3x = 90

5x = 90

x = 18

2(18)

mABD =

= 36°

3(18)

mDBC =

= 54°

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.

1 and 2

Linear pair

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.

1 and 3

Vertical angles

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.

2 and 4

Vertical angles

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.

5 and 7

neither

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.

5 and 8

neither

7. Find the values of x and y.

6x – 11 + 2x – 9 = 180

8x – 20 = 180

8x = 200

x = 25°

20y + 19 + 2x – 9 = 180

20y + 19 + 2(25) – 9 = 180

20y + 60 = 180

20y = 120

y = 6°

7. Find the values of x and y.

21x – 3 + 5x + 1 = 180

26x – 2 = 180

26x = 182

x = 7°

4y + 17y – 9 = 180

21y – 9 = 180

21y = 189

y = 9°

HW Problem

# 50

Vertical angles

Ans:

ex: AGB & EGD