GED Math : Supplementary Angles

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #1 : Supplementary Angles

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Refer to the above diagram. 

\(\displaystyle \overleftrightarrow{AE} ||\overleftrightarrow{BD}\)\(\displaystyle m \angle BCE = 136^{\circ }\). Evaluate \(\displaystyle m \angle CED\).

Possible Answers:

\(\displaystyle 46 ^{\circ }\)

\(\displaystyle 44 ^{\circ }\)

\(\displaystyle 56 ^{\circ }\)

\(\displaystyle 54 ^{\circ }\)

Correct answer:

\(\displaystyle 46 ^{\circ }\)

Explanation:

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

\(\displaystyle m \angle BCE + m\angle ECD =180^{\circ }\)

\(\displaystyle 136^{\circ } + m\angle ECD =180^{\circ }\)

\(\displaystyle m\angle ECD =180^{\circ } - 136 ^{\circ } = 44^{\circ }\)

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

\(\displaystyle m \angle CED + m\angle ECD =90^{\circ }\)

\(\displaystyle m \angle CED + 44 ^{\circ } =90^{\circ }\)

\(\displaystyle m \angle CED =90^{\circ } - 44 ^{\circ } = 46 ^{\circ }\)

Example Question #2 : Supplementary Angles

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

Possible Answers:

\(\displaystyle x= 14\)

\(\displaystyle x = 16\)

\(\displaystyle x = -2\)

\(\displaystyle x = 24\)

\(\displaystyle x = 10\)

Correct answer:

\(\displaystyle x= 14\)

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:

\(\displaystyle A + B + C =180\)

-or-

\(\displaystyle 5x + 15 + 2x + 25 + 2x + 15 = 180\)

 

Combine like terms and solve for \(\displaystyle x\):

\(\displaystyle 9x + 54 = 180\)

\(\displaystyle 9x = 126\)

\(\displaystyle x = 14\)

Example Question #3 : Supplementary Angles

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

Possible Answers:

No solution

\(\displaystyle x = -10\)

\(\displaystyle x = 15\)

\(\displaystyle x = 10\)

\(\displaystyle x = 5\)

Correct answer:

\(\displaystyle x = 10\)

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:

\(\displaystyle A + B = 180\)

-or-

\(\displaystyle 17x + 20 + -2x + 10 = 180\)

 

Combine like terms and solve for \(\displaystyle x\):

\(\displaystyle 15x + 30 = 180\)

\(\displaystyle 15x = 150\)

\(\displaystyle x = 10\)

Example Question #2 : Supplementary Angles

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

Possible Answers:

\(\displaystyle Angle A = 104^{\circ}\)

\(\displaystyle Angle B = 44^{\circ}\)

\(\displaystyle Angle C = 32^{\circ}\)

\(\displaystyle Angle A = 114^{\circ}\)

\(\displaystyle Anbgle B = 32^{\circ}\)

\(\displaystyle Angle C = 36^{\circ}\)

No solution

\(\displaystyle Angle A = 44^{\circ}\)

\(\displaystyle Angle B = 32^{\circ}\)

\(\displaystyle Angle C = 104^{\circ}\)

\(\displaystyle Angle A = 120^{\circ}\)

\(\displaystyle Angle B = 40^{\circ}\)

\(\displaystyle Angle C = 20^{\circ}\)

Correct answer:

\(\displaystyle Angle A = 104^{\circ}\)

\(\displaystyle Angle B = 44^{\circ}\)

\(\displaystyle Angle C = 32^{\circ}\)

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:

\(\displaystyle A + B + C = 180\)

-or-

\(\displaystyle 10x + 4 + 5x - 6 + 3x + 2 = 180\)

 

Combine like terms and solve for x:

\(\displaystyle 18x = 180\)

\(\displaystyle x = 10\)

 

Plug \(\displaystyle x\) back into the three angle measurements:

\(\displaystyle Angle A = 10(10) + 4\)

\(\displaystyle Angle A = 100 + 4\) 4

\(\displaystyle Angle A = 104\)

 

\(\displaystyle Angle B = 5(10) - 6\)

\(\displaystyle Angle B = 50 -6\)

\(\displaystyle Angle B = 46\)

 

\(\displaystyle Angle C = 3(10) + 2\)

\(\displaystyle Angle C = 30 + 2\)

\(\displaystyle Angle C = 32\)

Example Question #2 : Supplementary Angles

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

Possible Answers:

\(\displaystyle 31\)

\(\displaystyle 89\)

\(\displaystyle 99\)

\(\displaystyle 79\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 79\)

Explanation:

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

To find the other angle, subtract 101 from 180.

\(\displaystyle 180-101=79\)

The answer is:  \(\displaystyle 79\)

Example Question #2 : Supplementary Angles

What angle is supplementary to 54 degrees?

Possible Answers:

\(\displaystyle 126\)

\(\displaystyle 136\)

\(\displaystyle 16\)

\(\displaystyle 116\)

\(\displaystyle 26\)

Correct answer:

\(\displaystyle 126\)

Explanation:

Supplementary angles must add up to 180 degrees.

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

\(\displaystyle 180-54 = 126\)

The answer is:  \(\displaystyle 126\)

Example Question #1 : Supplementary Angles

If \(\displaystyle 2x\) and \(\displaystyle 8x\) are supplementary angles, what must be a possible angle?

Possible Answers:

\(\displaystyle 64\)

\(\displaystyle 160\)

\(\displaystyle 18\)

\(\displaystyle 144\)

\(\displaystyle 120\)

Correct answer:

\(\displaystyle 144\)

Explanation:

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

Set up the equation.

\(\displaystyle 2x+8x = 180\)

Solve for \(\displaystyle x\).

\(\displaystyle 10x = 180\)

Divide by 10 on both sides.

\(\displaystyle \frac{10x }{10}= \frac{180}{10}\)

\(\displaystyle x=18\)

Substitute \(\displaystyle x=18\) for \(\displaystyle 2x\) and \(\displaystyle 8x\), and we have 36 and 144, which add up to 180.

The answer is:  \(\displaystyle 144\)

Example Question #2 : Supplementary Angles

If the angles \(\displaystyle x+1\) and \(\displaystyle 2x-1\) are supplementary, what is the value of \(\displaystyle 3x\)?

Possible Answers:

\(\displaystyle 30\)

\(\displaystyle 61\)

\(\displaystyle 90\)

\(\displaystyle 180\)

\(\displaystyle 60\)

Correct answer:

\(\displaystyle 180\)

Explanation:

Supplementary angles sum to 180 degrees.

Set up an equation to solve for \(\displaystyle x\).

\(\displaystyle x+1+2x-1 = 180\)

\(\displaystyle 3x = 180\)

\(\displaystyle x=60\)

Substitute this value to \(\displaystyle 3x\).

\(\displaystyle 3(60) = 180\)

The answer is:  \(\displaystyle 180\)

Example Question #3 : Supplementary Angles

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

Possible Answers:

\(\displaystyle 87\)

\(\displaystyle 93\)

\(\displaystyle 186-2x\)

\(\displaystyle 2x-186\)

\(\displaystyle 174-2x\)

Correct answer:

\(\displaystyle 186-2x\)

Explanation:

Supplementary angles add up to 180 degrees.

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

\(\displaystyle 180-(2x-6)\)

Distribute the negative.

\(\displaystyle 180-2x+6 = 186-2x\)

The answer is:  \(\displaystyle 186-2x\)

Example Question #4 : Supplementary Angles

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

Possible Answers:

\(\displaystyle \frac{2}{3}\pi\)

\(\displaystyle 2\pi\)

\(\displaystyle \frac{4}{3}\pi\)

\(\displaystyle \frac{1}{3}\pi\)

\(\displaystyle \frac{5}{3}\pi\)

Correct answer:

\(\displaystyle \frac{1}{3}\pi\)

Explanation:

Note that supplementary angles sum up to 180 degrees or equal to \(\displaystyle \pi\) radians.

Subtract the known angle from pi.

\(\displaystyle \pi-\frac{2}{3}\pi = \frac{1}{3}\pi\)

The answer is:  \(\displaystyle \frac{1}{3}\pi\)

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