Complementary and Supplementary Angles

Show your work for each problem.

1.
Two angles are complementary. What is their sum?
1. a)
2. b)
3. c)
4. d)
Answer:
Complementary angles always add up to , which is a right angle. Supplementary angles add up to .
2.
Two angles are supplementary. What is their sum?
1. a)
2. b)
3. c)
4. d)
Answer:
Supplementary angles always add up to , which is a straight angle. This is different from complementary angles which add up to .
3.
Find the complement of .
Answer: 50
The complement of is . Complementary angles always add up to .
4.
Find the supplement of .
Answer: 115
The supplement of is . Supplementary angles always add up to .
5.
Which of the following pairs are complementary angles?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
, so these are complementary. The other pairs sum to , making them supplementary, not complementary.
6.
Find the complement of .
Answer: 17
The complement of is .
7.
Find the supplement of .
Answer: 38
The supplement of is .
8.
An angle is more than its complement. What is the angle?
1. a)
2. b)
3. c)
4. d)
Answer:
Let the angle be . Its complement is . Given: . Solving: , so . Check: and .
9.
Two complementary angles are in the ratio . Find both angles.
Answer: 18, 72
1. Let the angles be and . What is their sum? 90
2. Write the equation: 5x
3. Solve . What is ? 18
4. Find . What is the larger angle? 72
10.
Two supplementary angles are in the ratio . Find both angles.
Answer: 40, 140
1. Let the angles be and . What is their sum? 180
2. Write the equation: 9x
3. Solve . What is ? 20
4. Find both angles: and 40, 140
11.
The supplement of an angle is more than twice the angle. Find the angle.
Answer: 50
1. Let the angle be . The supplement is . What equation represents 'supplement = 2x + 30'? 180-x = 2x + 30
2. Solve for x: . First, add x to both sides. What do you get? 180 = 3x + 30
3. Now subtract 30 from both sides: 150 = 3x
4. Divide by 3 to find x: 50
12.
The complement of an angle is less than the angle. Find the angle.
Answer: 48
Let the angle be . Complement = . Given: . Solving: , so , thus . Check: complement is , which is less than .
13.
The supplement of an angle is 4 times its complement. Find the angle.
Answer: 60
1. Let the angle be . What is its supplement? 180-x
2. What is its complement? 90-x
3. Set up the equation: supplement = 4 times complement 180-x = 4(90-x)
4. Expand and solve: . What is ? 60
14.
Can an obtuse angle have a complement?
1. a)Only if both angles are adjacent
2. b)Yes, any angle has a complement
3. c)No, because it would require a negative angle
4. d)Only if it's less than 135 degrees
Answer: No, because it would require a negative angle
An obtuse angle is greater than . To have a complement, you need , which would be a negative angle. Negative angles are not defined for standard geometry, so obtuse angles cannot have complements.
15.
Two angles form a linear pair. One angle is 5 times the other. Find both angles.
Answer: 30, 150
1. A linear pair is supplementary. What do they add up to? 180
2. Let one angle be . The other is . Write the equation: x + 5x = 180
3. Simplify to . What is ? 30
4. Find . What is the larger angle? 150