1.5 âDescribe Angle Pair Relationships

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# 1.5 âDescribe Angle Pair Relationships - PowerPoint PPT Presentation

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. m 1 + m 2 = 90 °. Supplementary Angles:. Two angles that add to 180 °. 2. 1. 1.

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Two angles that share a common side and vertex

2

1

Complementary Angles:

Two angles that add to 90°

1

2

1

2

m1 + m2 = 90°

Supplementary Angles:

Two angles that add to 180°

2

1

1

m1 + m2 = 180°

2

Two adjacent angles whose noncommon sides are opposite rays

Linear Pair:

2

1

They will always add to 180°

m1 + m2 = 180°

Vertical Angles:

Two angles whose sides form two pairs of opposite rays

1

2

They will always be congruent!

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 m2.

m1 = 82°

m2 =

90 – 82 =

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

m1 = 23°

m2 =

90 – 23 =

67°

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

m1 = 82°

m2 =

180 – 82 =

98°

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

m1 = 105°

m2 =

180 – 105 =

75°

5. Find the measure of ABD and DBC.

4x + 6 + 11x – 6 = 180

15x = 180

x = 12

4(12)+6

mABD =

= 48+6

= 54°

11(12)-6

mDBC =

= 132-6

= 126°

5. Find the measure of ABD and DBC.

2x + 3x = 90

5x = 90

x = 18

2(18)

mABD =

= 36°

3(18)

mDBC =

= 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