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GED Math : Complementary Angles

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Example Questions

Example Question #21 : Complementary Angles

Angles a and b are complementary. If $a= 70^{\circ}$ , find b.

Possible Answers:

$b=70^{\circ}$

$b=110^{\circ}$

$b=10^{\circ}$

$b=190^{\circ}$

$b=20^{\circ}$

Correct answer:

$b=20^{\circ}$

Explanation:

Two angles are complementary if they add up to $90^{\circ}$ . So, we will use the following formula:

$a+b=90^{\circ}$

We know $a= 70^{\circ}$ , so we will substitute and solve for b. We get

$70^{\circ} + b = 90^{\circ}$

$70^{\circ} - 70^{\circ}+b=90^{\circ}-70^{\circ}$

$0^{\circ}+b=20^{\circ}$

$b=20^{\circ}$

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Example Question #22 : Complementary Angles

If two angles are complementary, and one angle is measured 90-90x degrees, what must be the other angle?

Possible Answers:

90x

90x-90

-90x

180-90x

180x

Correct answer:

90x

Explanation:

Complementary angles sum up to degrees.

Simply subtract the given angle from to determine the expression.

90-(90-90x) = 90-90+90x

Combine like-terms.

The answer is: 90x

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Example Question #21 : Complementary Angles

Suppose two angles are complementary. If an angle is $\frac{\pi}{4}$ radians, what must be the value of the other angle?

Possible Answers:

$\frac{1}{4}\pi$

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

$\frac{1}{2}\pi$

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

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

Correct answer:

$\frac{1}{4}\pi$

Explanation:

Recall that $\pi \textup{ rad} = 180 \textup{ deg}$ .

Complementary angles sum up to 90 degrees, or $\frac{\pi}{2} \textup{ rad}$ .

To find the other angle, subtract $\frac{\pi}{4}$ radians from $\frac{\pi}{2}$ radians.

$\frac{\pi}{2} -\frac{\pi}{4} = \frac{2\pi}{4} -\frac{\pi}{4} =\frac{\pi}{4}$

The answer is: $\frac{1}{4}\pi$

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Example Question #21 : Angle Geometry

Suppose two angles are complementary. If an angle is measured $\frac{35}{3}$ degrees, what is the other angle?

Possible Answers:

$\frac{505}{3}$

$\frac{45}{2}$

$\frac{235}{6}$

$\textup{The answer is not given.}$

$\frac{235}{3}$

Correct answer:

$\frac{235}{3}$

Explanation:

The sum of both angles will be 90 degrees since they are complementary.

Subtract the given angle from 90.

$90-\frac{35}{3} = \frac{270}{3} - \frac{35}{3} = \frac{235}{3}$

The answer is: $\frac{235}{3}$

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Example Question #21 : Complementary Angles

Two angles are complementary if they add up to:

Possible Answers:

$270^{\circ}$

$45^{\circ}$

$360^{\circ}$

$90^{\circ}$

$180^{\circ}$

Correct answer:

$90^{\circ}$

Explanation:

Two angles are complementary if they add up to $90^{\circ}$ .

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Example Question #23 : Angle Geometry

Two angles are complementary. If the first angle is $28^{\circ}$ , what is the value of the second angle?

Possible Answers:

$62^{\circ}$

$17^{\circ}$

$152^{\circ}$

$332^{\circ}$

$197^{\circ}$

Correct answer:

$62^{\circ}$

Explanation:

Two angles are complementary if they add up to $90^{\circ}$ . So, we can write it as the formula:

$a + b = 90^{\circ}$

Now, we know one angle is $28^{\circ}$ . So, we can substitute and solve for the other angle. So, we get

$a + 28^{\circ} =90^{\circ}$

$a+28^{\circ} - 28^{\circ} = 90^{\circ} - 28^{\circ}$

$a+0^{\circ} = 62^{\circ}$

$a=62^{\circ}$

Therefore, the other angle is $62^{\circ}$ .

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Example Question #22 : Complementary Angles

What angle is complementary to 80 degrees?

Possible Answers:

160

100

170

Correct answer:

Explanation:

Complementary angles must add up to 90 degrees.

To find the other angle, we must subtract 80 from 90 degrees.

90-80 = 10

The answer is:

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Example Question #26 : Complementary Angles

Suppose two angles are complementary. If one angle measurement is $\frac{1}{8}\pi$ radians, what must be the other angle?

Possible Answers:

$\frac{3}{8}\pi$

$\frac{1}{8}\pi$

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

$\frac{4}{8}\pi$

$\frac{5}{8}\pi$

Correct answer:

$\frac{3}{8}\pi$

Explanation:

Complementary angles sum up to 90 degrees, or $\frac{\pi}{2}$ radians.

Subtract $\frac{1}{8}\pi$ radians from $\frac{\pi}{2}$ radians.

$\frac{\pi}{2}-\frac{\pi}{8} = \frac{4\pi}{8}-\frac{\pi}{8} = \frac{3}{8}\pi$

The answer is: $\frac{3}{8}\pi$

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Example Question #23 : Complementary Angles

Suppose two angles are complementary. If one angle measurement is 52 degrees, what is the other angle?

Possible Answers:

148

120

138

Correct answer:

Explanation:

Complementary angles sum up to 90 degrees.

Subtract the known angle from 90.

90-52 = 38

The answer is:

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Example Question #24 : Complementary Angles

Suppose two angles are complementary. What is the value of the other angle if a known angle is 43 degrees?

Possible Answers:

137

157

Correct answer:

Explanation:

Complementary angles must add up to 90 degrees.

Subtract the known angle from 90.

90-43 = 47

The answer is:

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GED Math : Complementary Angles

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Complementary Angles

Example Question #22 : Complementary Angles

Example Question #21 : Complementary Angles

Example Question #21 : Angle Geometry

Example Question #21 : Complementary Angles

Example Question #23 : Angle Geometry

Example Question #22 : Complementary Angles

Example Question #26 : Complementary Angles

Example Question #23 : Complementary Angles

Example Question #24 : Complementary Angles

All GED Math Resources

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