Angle Relationships&

Parallel LinesPre-Algebra

Adjacent angles are “side by side” and share a common ray.

45º15º

These are examples of adjacent angles.

55º

35º

50º130º

80º 45º

85º20º

These angles are NOT adjacent.

45º55º

50º100º

35º

35º

Complementary Anglessum to 90°

40°

50°

Complementary angles add up to 90º.

60º

30º40º

50º

Adjacent and Complementary Angles

Complementary Anglesbut not Adjacent

Supplementary Anglessum to 180°

30° 150°

Supplementary angles add up to 180º.

60º120º

40º

140º

Adjacent and Supplementary Angles

Supplementary Anglesbut not Adjacent

Vertical Anglesare opposite one another.

Vertical angles are congruent.

100°

100°

Vertical Anglesare opposite one another.

Vertical angles are congruent.

80°

80°

Lines l and m are parallel.l||m

120°

l

m

120°

120°

120°

Note the 4 angles that measure 120°.

nLine n is a transversal.

Lines l and m are parallel.l||m

60°

l

m

60°

60°

60°

Note the 4 angles that measure 60°.

nLine n is a transversal.

Lines l and m are parallel.l||m

60°

l

m

60°

60°

60°

There are many pairs of angles that are supplementary.

There are 4 pairs of angles that are vertical.

120°

120°

120°

120°

nLine n is a transversal.

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.

Practice Time!

1) Find the missing angle.

36°

?°

1) Find the missing angle.

36°

?°

90 ° – 36 = 54°

2) Find the missing angle.

64°

?°

2) Find the missing angle.

64°

?°

90 ° – 64° = 26°

3) Solve for x.

3x°

2x°

3) Solve for x.

3x°

2x°

3x° + 2x° = 90°

5x = 90

x =18

4) Solve for x.

2x + 5

x + 25

4) Solve for x.

2x + 5

x + 25

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

3x + 30 = 90

3x = 60

x = 20

5) Find the missing angle.

?° 168°

5) Find the missing angle.

?° 168°

180° – 168° = 12°

6) Find the missing angle.

58° ?°

6) Find the missing angle.

58° ?°

180° – 58° = 122°

7) Solve for x.

4x 5x

7) Solve for x.

4x 5x

4x + 5x = 180

9x = 180

x = 20

8) Solve for x.

2x + 10 3x + 20

8) Solve for x.

2x + 10 3x + 20

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

5x + 30 = 180

5x = 150

x = 30

9) Lines l and m are parallel.l||m

Find the missing angles.

42°

l

m

b°

d°

f°

a °

c°

e°

g°

9) Lines l and m are parallel.l||m

Find the missing angles.

42°

l

m

42°

42°

42°

138°

138°

138°

138°

10) Lines l and m are parallel.l||m

Find the missing angles.

81°

l

m

b°

d°

f°

a °

c°

e°

g°

10) Lines l and m are parallel.l||m

Find the missing angles.

81°

l

m

81°

81°

81°

99°

99°

99°

99°

11) Find the missing angles.

70 °b°

70 °

d ° 65 °

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

11) Find the missing angles.

70 °40°

70 °

75 ° 65 °

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

12) Find the missing angles.

45 °b°

50 °

d ° 75 °

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

12) Find the missing angles.

45 °85°

50 °

20° 75 °

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

In the figure a || b.

13. Name the angles congruent to 3.

14. Name all the angles supplementary to 6.

15. If m1 = 105° what is m3?

16. If m5 = 120° what is m2?

1, 5, 7

1, 3, 5, 7

105°

60°

The End