Angle Relationships

Pre-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°

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

(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) Find the missing angles.

42°

lb°

a °

c°

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

Find the missing angles.

42°

l42°

138°

138°

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

Find the missing angles.

81°

lb°

a °

c°

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

Find the missing angles.

81°

l81°

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 m?

1, 5, 7

1, 3, 5, 7

105°

60°

The End