2-Dimensional Geometry - GED Math

Card 0 of 2760

Question

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

Answer

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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Question

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

Answer

Complementary angles sum up to 90 degrees.

Subtract the known angle from 90.

The answer is:

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Question

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

Answer

Complementary angles must add up to 90 degrees.

Subtract the known angle from 90.

The answer is:

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Question

Use the following angles to answer the question:

If these two angles are complementary, find the value of x.

Answer

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

$x+y = 90^{\circ}$

where x and y are the angles.

So, given the angles

we can see one angle is $73^{\circ}$ . So, we can substitute and solve for x. We get

$x + 73^{\circ}=90^{\circ}$

$x+73^{\circ}-73^{\circ}=90^{\circ}-73^{\circ}$

$x+0^{\circ}=17^{\circ}$

$x=17^{\circ}$

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Question

If angle measure is degrees, what is the other angle if both angles are complementary?

Answer

Complementary angles add up to 90 degrees.

To determine the other angle, subtract 81 from 90.

The answer is:

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Question

If two angles are complementary, and one angle is $75^{\circ}$ , what is the value of the other angle?

Answer

Two angles are complementary if they add up to $90^{\circ}$ . We can use the formula:

$x+y=90^{\circ}$

where x and y are the angles.

Now, we know one angle is $75^{\circ}$ . So, we will substitute and solve for the other angle. We get

$x+75^{\circ}=90^{\circ}$

$x+75^{\circ}-75^{\circ}=90^{\circ}-75^{\circ}$

$x+0^{\circ} = 15^{\circ}$

$x=15^{\circ}$

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Question

If an angle is measured 35 degrees, what is the other angle if both angles are complementary?

Answer

Complementary angles sum up to 90 degrees.

To find the other angle, subtract the known angle from 90 degrees.

The answer is:

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Question

Suppose two angles are complementary. What must be if the angles are and degrees?

Answer

The sum of both angles must add up to 90 degrees.

Solve for the variable.

Add 5 on both sides.

Divide by 10 on both sides.

$\frac{10x}{10}=\frac{95}{10}$

Simplify the fraction.

The answer is: $\frac{19}{2}$

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Question

If two angles are complementary, and one angle is measured $\frac{\pi}{3}$ radians, what is the other angle in radians?

Answer

If the set of angles are complementary, they must add up to $\frac{\pi}{2}$ radians, which is equivalent to 90 degrees.

Subtract $\frac{\pi}{3}$ radians from $\frac{\pi}{2}$ radians.

$\frac{\pi}{2}-\frac{\pi}{3} = \frac{3\pi}{6}-\frac{2\pi}{6}$

The answer is: $\frac{1}{6}\pi$

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Question

Which angle is complementary to 30 degrees?

Answer

Complementary angles must sum up to 90 degrees. In order to find the other angle, we must subtract the given angle from 90 degrees.

The answer is:

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Question

Which of the following pairs of angles are complementary angles?

Answer

Which of the following pairs of angles are complementary angles?

Recall that complementary angles are angles which add up to 90 degrees.

In this case, all we have to do is see which pairs sum to 90, and that will be our answer:

$38^{\circ}+42^{\circ}=80^{\circ}$

$39^{\circ}+151^{\circ}=190^{\circ}$

$139^{\circ}+41^{\circ}=180^{\circ}$

$39^{\circ} + 51^{\circ}=90^{\circ}$

So it must be the last one.

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Question

Right triangle $\bigtriangleup ABC$ has right angle $\angle B$ and $23^{\circ }$ angle $\angle A$ . What would be the measure of an angle which is complementary to $\angle C$ ?

Answer

No calculation is actually required for this problem. $\angle B$ is the right angle of $\bigtriangleup ABC$ , so $\angle A$ and $\angle C$ must comprise a complementary pair of angles. Since $\angle A$ is complementary to $\angle C$ , any angle complementary to $\angle C$ must have measure equal to that of $\angle A$ , which is $23^{\circ }$ .

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Question

The image is not to scale.

If the sum of two angles results in a complementary angle, what is the measure of the unknown angle?

Answer

With the provided image, we are asked to solve for the measure of the unknown angle.

First, we must understand some information before attempting to solve the problem. The problem provides the information that the two angles summed up result in a complimentary angle. This is another way to say that when we add the measures of the two angles, it will equal $90^{\circ}$ .

This becomes a problem where we solve for a missing variable now. We can call the unknown angle x. We would set this up in equation format accordingly:

Now, we can solve for x.

$x+30{\color{Red} -30}=90{\color{Red} -30}$

$x=60^{\circ}$

Therefore, the unknown angle is $60^{\circ}$ .

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Question

The image is not to scale.

If the sum of two angles results in a complementary angle, what is the measure of the unknown angle?

Answer

With the provided image, we are asked to solve for the measure of the unknown angle.

First, we must understand some information before attempting to solve the problem. The problem provides the information that the two angles summed up result in a complimentary angle. This is another way to say that when we add the measures of the two angles, it will equal $90^{\circ}$ .

This becomes a problem where we solve for a missing variable now. We can call the unknown angle x. We would set this up in equation format accordingly:

Now, we can solve for x.

$x+72{\color{Red} -72}=90{\color{Red} -72}$

$x=18^{\circ}$

Therefore, the unknown angle is $18^{\circ}$ .

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Question

The image is not to scale.

If the sum of two angles results in a complementary angle, what is the measure of the unknown angle?

Answer

With the provided image, we are asked to solve for the measure of the unknown angle.

First, we must understand some information before attempting to solve the problem. The problem provides the information that the two angles summed up result in a complimentary angle. This is another way to say that when we add the measures of the two angles, it will equal $90^{\circ}$ .

This becomes a problem where we solve for a missing variable now. We can call the unknown angle x. We would set this up in equation format accordingly:

Now, we can solve for x.

$x+63{\color{Red} -63}=90{\color{Red} -63}$

$x=27^{\circ}$

Therefore, the unknown angle is $27^{\circ}$ .

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Question

Which of the following angles forms a complementary angle pair with $\measuredangle D$ ?

Given that $\measuredangle D= 57^{\circ}$

Answer

Which of the following angles forms a complementary angle pair with $\measuredangle D$ ?

Given that $\measuredangle D= 57^{\circ}$

Complementary angles sum up to 90 degrees. Therefore, to find our answer, we simply need to do the following:

$90^{\circ}-57^{\circ}=33^{\circ}$

So, our answer is 33 degrees

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Question

Find the the measure of angle B if it is complement of angle A:

$m\angle A=75^{o}$

Answer

If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:

$m\angle B=90^{o}-75^{o}=15^{o}$

This gives us a final answer of 15 degrees for angle B.

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Question

Find the the measure of angle B if it is complement of angle A:

$m\angle A=27^{o}$

Answer

If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:

$m\angle B=90^{o}-27^{o}=63^{o}$

This gives us a final answer of 63 degrees for angle B.

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Question

Find the the measure of angle B if it is complement of angle A:

$m\angle A=48^{o}$

Answer

If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:

$m\angle B=90^{o}-48^{o}=42^{o}$

This gives us a final answer of 42 degrees for angle B.

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Question

Find the the measure of angle B if it is complement of angle A:

$m\angle A=6^{o}$

Answer

If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:

$m\angle B=90^{o}-6^{o}=84^{o}$

This gives us a final answer of 84 degrees for angle B.

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