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GED Math : Supplementary Angles

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Example Question #1 : Supplementary Angles

Thingy

Refer to the above diagram.

$\overleftrightarrow{AE} ||\overleftrightarrow{BD}$ ; $m \angle BCE = 136^{\circ }$ . Evaluate $m \angle CED$ .

Possible Answers:

$54 ^{\circ }$

$56 ^{\circ }$

$46 ^{\circ }$

$44 ^{\circ }$

Correct answer:

$46 ^{\circ }$

Explanation:

$\angle BCE$ and $\angle ECD$ form a linear pair, so they are supplementary - that is, their degree measures total $180^{\circ }$ , so

$m \angle BCE + m\angle ECD =180^{\circ }$

$136^{\circ } + m\angle ECD =180^{\circ }$

$m\angle ECD =180^{\circ } - 136 ^{\circ } = 44^{\circ }$

$m \angle CED$ and $\angle ECD$ are acute angles of right triangle $\Delta ECD$ , so they are complementary - that is, their degree measures total $90^{\circ }$ , so

$m \angle CED + m\angle ECD =90^{\circ }$

$m \angle CED + 44 ^{\circ } =90^{\circ }$

$m \angle CED =90^{\circ } - 44 ^{\circ } = 46 ^{\circ }$

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Example Question #2 : Supplementary Angles

Angles A, B, and C are supplementary. The measure of angle A is 5x + 15 . The measure of angle B is 2x + 25 . The measure for angle C is 2x + 14 . Find the value of .

Possible Answers:

x = 10

x= 14

x = -2

x = 24

x = 16

Correct answer:

x= 14

Explanation:

Since angles A, B, and C are supplementary, their measures add up to equal 180 degrees. Therefore we can set up the equation as such:

A + B + C =180

-or-

5x + 15 + 2x + 25 + 2x + 15 = 180

Combine like terms and solve for :

9x + 54 = 180

9x = 126

x = 14

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Example Question #3 : Supplementary Angles

Angles A and B are supplementary. The measure of angle A is 17x + 20 . The measure of Angle B is -2x + 10 . Find the value of .

Possible Answers:

x = 15

No solution

x = -10

x = 5

x = 10

Correct answer:

x = 10

Explanation:

Since angles A and B are supplementary, thier measurements add up to equal 180 degrees. Therefore we can set up our equation like such:

A + B = 180

-or-

17x + 20 + -2x + 10 = 180

Combine like terms and solve for :

15x + 30 = 180

15x = 150

x = 10

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Example Question #4 : Supplementary Angles

Angles A, B, and C are supplementary. The measure of angle A is 10x + 4 . The measure of angle B is 5x - 6 . The measure for angle C = 3x + 2 . What are the measure for the three angles?

Possible Answers:

$Angle A = 114^{\circ}$

$Anbgle B = 32^{\circ}$

$Angle C = 36^{\circ}$

$Angle A = 104^{\circ}$

$Angle B = 44^{\circ}$

$Angle C = 32^{\circ}$

$Angle A = 44^{\circ}$

$Angle B = 32^{\circ}$

$Angle C = 104^{\circ}$

$Angle A = 120^{\circ}$

$Angle B = 40^{\circ}$

$Angle C = 20^{\circ}$

No solution

Correct answer:

$Angle A = 104^{\circ}$

$Angle B = 44^{\circ}$

$Angle C = 32^{\circ}$

Explanation:

Since angles A, B, and C are supplementary, their measures add up to equal 180 degrees. Therefore we can set up an equation as such:

A + B + C = 180

-or-

10x + 4 + 5x - 6 + 3x + 2 = 180

Combine like terms and solve for x:

18x = 180

x = 10

Plug back into the three angle measurements:

Angle A = 10(10) + 4

Angle A = 100 + 4 4

Angle A = 104

Angle B = 5(10) - 6

Angle B = 50 -6

Angle B = 46

Angle C = 3(10) + 2

Angle C = 30 + 2

Angle C = 32

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Example Question #1 : Supplementary Angles

If a set of angles are supplementary, what is the other angle if one angle is 101 degrees?

Possible Answers:

Correct answer:

Explanation:

Two angles that are supplementary must add up to 180 degrees.

To find the other angle, subtract 101 from 180.

180-101=79

The answer is:

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Example Question #1 : Supplementary Angles

What angle is supplementary to 54 degrees?

Possible Answers:

126

116

136

Correct answer:

126

Explanation:

Supplementary angles must add up to 180 degrees.

To find the other angle, we will need to subtract 54 from 180.

180-54 = 126

The answer is: 126

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Example Question #7 : Supplementary Angles

If and are supplementary angles, what must be a possible angle?

Possible Answers:

144

120

160

Correct answer:

144

Explanation:

The sum of the two angles supplement to each other will add up to 180 degrees.

Set up the equation.

2x+8x = 180

Solve for .

10x = 180

Divide by 10 on both sides.

$\frac{10x }{10}= \frac{180}{10}$

x=18

Substitute x=18 for and , and we have 36 and 144, which add up to 180.

The answer is: 144

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Example Question #8 : Supplementary Angles

If the angles x+1 and 2x-1 are supplementary, what is the value of ?

Possible Answers:

180

Correct answer:

180

Explanation:

Supplementary angles sum to 180 degrees.

Set up an equation to solve for .

x+1+2x-1 = 180

3x = 180

x=60

Substitute this value to .

3(60) = 180

The answer is: 180

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Example Question #9 : Supplementary Angles

Suppose there are two angles. If a given angle is 2x-6 , and both angles are supplementary, what must be the other angle?

Possible Answers:

2x-186

174-2x

186-2x

Correct answer:

186-2x

Explanation:

Supplementary angles add up to 180 degrees.

This means we will need to subtract the known angle quantity from 180.

180-(2x-6)

Distribute the negative.

180-2x+6 = 186-2x

The answer is: 186-2x

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Example Question #10 : Supplementary Angles

If an angle given is $\frac{2}{3}\pi$ radians, what is the other angle if both angles are supplementary?

Possible Answers:

$\frac{1}{3}\pi$

$\frac{4}{3}\pi$

$\frac{5}{3}\pi$

$2\pi$

$\frac{2}{3}\pi$

Correct answer:

$\frac{1}{3}\pi$

Explanation:

Note that supplementary angles sum up to 180 degrees or equal to $\pi$ radians.

Subtract the known angle from pi.

$\pi-\frac{2}{3}\pi = \frac{1}{3}\pi$

The answer is: $\frac{1}{3}\pi$

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GED Math : Supplementary Angles

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Supplementary Angles

Example Question #2 : Supplementary Angles

Example Question #3 : Supplementary Angles

Example Question #4 : Supplementary Angles

Example Question #1 : Supplementary Angles

Example Question #1 : Supplementary Angles

Example Question #7 : Supplementary Angles

Example Question #8 : Supplementary Angles

Example Question #9 : Supplementary Angles

Example Question #10 : Supplementary Angles

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