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Angle Relationships & Parallel Lines. Pre-Algebra. Adjacent angles are “side by side” and share a common ray. 15 º. 45 º. These are examples of adjacent angles. 45 º. 80 º. 35 º. 55 º. 130 º. 50 º. 85 º. 20 º. These angles are NOT adjacent. 100 º. 50 º. 35 º. 35 º. 55 º. 45 º.

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these are examples of adjacent angles
These are examples of adjacent angles.

45º

80º

35º

55º

130º

50º

85º

20º

these angles are not adjacent
These angles are NOT adjacent.

100º

50º

35º

35º

55º

45º

slide6

Complementary angles add up to 90º.

30º

40º

50º

60º

Adjacent and Complementary Angles

Complementary Anglesbut not Adjacent

slide8

Supplementary angles add up to 180º.

40º

120º

60º

140º

Adjacent and Supplementary Angles

Supplementary Anglesbut not Adjacent

slide11

Lines l and m are parallel.l||m

Note the 4 angles that measure 120°.

120°

120°

l

120°

120°

m

Line n is a transversal.

n

slide12

Lines l and m are parallel.l||m

Note the 4 angles that measure 60°.

60°

60°

l

60°

60°

m

Line n is a transversal.

n

slide13

Lines l and m are parallel.l||m

There are 4 pairs of angles that are vertical.

There are many pairs of angles that are supplementary.

60°

120°

120°

60°

l

60°

120°

120°

60°

m

Line n is a transversal.

n

slide14

If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.

slide17

1) Find the missing angle.

36°

90 ° – 36 = 54°

slide19

2) Find the missing angle.

64°

90 ° – 64° = 26°

slide21

3) Solve for x.

2x°

3x°

3x° + 2x° = 90°

5x = 90

x =18

slide22

4) Solve for x.

x + 25

2x + 5

slide23

4) Solve for x.

x + 25

2x + 5

(2x + 5) + (x + 25) = 90

3x + 30 = 90

3x = 60

x = 20

slide25

5) Find the missing angle.

168°

180° – 168° = 12°

slide27

6) Find the missing angle.

58°

180° – 58° = 122°

slide29

7) Solve for x.

5x

4x

4x + 5x = 180

9x = 180

x = 20

slide30

8) Solve for x.

3x + 20

2x + 10

slide31

8) Solve for x.

3x + 20

2x + 10

(2x + 10) + (3x + 20) = 180

5x + 30 = 180

5x = 150

x = 30

slide36

11) Find the missing angles.

70 °

70 °

Hint: The 3 angles in a triangle sum to 180°.

d °

65 °

slide37

11) Find the missing angles.

70 °

70 °

40°

Hint: The 3 angles in a triangle sum to 180°.

75 °

65 °

slide38

12) Find the missing angles.

45 °

50 °

Hint: The 3 angles in a triangle sum to 180°.

d °

75 °

slide39

12) Find the missing angles.

45 °

50 °

85°

Hint: The 3 angles in a triangle sum to 180°.

20°

75 °

slide40

In the figure a || b.

13. Name the angles congruent to 3.

1, 5, 7

14. Name all the angles supplementary to 6.

1, 3, 5, 7

15. If m1 = 105° what is m3?

105°

16. If m5 = 120° what is m2?

60°