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Example Questions

Example Question #56 : Complementary Angles

If an angle measures 23.5 $\displaystyle 23.5$ degrees, find the measurement of the other angle such that the two angles are complementary.

Possible Answers:

75.5 $\displaystyle 75.5$

67.5 $\displaystyle 67.5$

66.5 $\displaystyle 66.5$

65.5 $\displaystyle 65.5$

Correct answer:

66.5 $\displaystyle 66.5$

Explanation:

Two angles are classified as complementary if an only if the sum of the angles equals to exactly 90 degrees.

Since we know the measurement of one angle, and we know the rule about complementary angles, let's find the other angle:

The other angle is simply the total sum of both angles minus the given angle.
The total sum of the angles is $\displaystyle 90$, and the given angle is 23.5 $\displaystyle 23.5$.

So, we will subtract 23.5 $\displaystyle 23.5$ from $\displaystyle 90$.

Other angle=$\displaystyle 90-23.5=66.5$

The other angle has a measurement of 66.5 $\displaystyle 66.5$ degrees.

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Example Question #51 : Angle Geometry

Thingy

Refer to the above diagram.

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

Possible Answers:

$56 ^{\circ }$ $\displaystyle 56 ^{\circ }$

$46 ^{\circ }$ $\displaystyle 46 ^{\circ }$

$44 ^{\circ }$ $\displaystyle 44 ^{\circ }$

$54 ^{\circ }$ $\displaystyle 54 ^{\circ }$

Correct answer:

$46 ^{\circ }$ $\displaystyle 46 ^{\circ }$

Explanation:

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

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

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

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

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

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

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

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

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Example Question #2 : Supplementary Angles

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

Possible Answers:

x = 24 $\displaystyle x = 24$

x = 16 $\displaystyle x = 16$

x = -2 $\displaystyle x = -2$

x= 14 $\displaystyle x= 14$

x = 10 $\displaystyle x = 10$

Correct answer:

x= 14 $\displaystyle x= 14$

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 $\displaystyle x$:

$\displaystyle 9x + 54 = 180$

$\displaystyle 9x = 126$

x = 14 $\displaystyle x = 14$

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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:

x = 5 $\displaystyle x = 5$

x = 15 $\displaystyle x = 15$

x = 10 $\displaystyle x = 10$

x = -10 $\displaystyle x = -10$

No solution

Correct answer:

x = 10 $\displaystyle x = 10$

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 $\displaystyle x$:

$\displaystyle 15x + 30 = 180$

$\displaystyle 15x = 150$

x = 10 $\displaystyle x = 10$

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Example Question #4 : Supplementary Angles

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

Possible Answers:

$Angle A = 104^{\circ}$ $\displaystyle Angle A = 104^{\circ}$

$Angle B = 44^{\circ}$ $\displaystyle Angle B = 44^{\circ}$

$Angle C = 32^{\circ}$ $\displaystyle Angle C = 32^{\circ}$

$Angle A = 120^{\circ}$ $\displaystyle Angle A = 120^{\circ}$

$Angle B = 40^{\circ}$ $\displaystyle Angle B = 40^{\circ}$

$Angle C = 20^{\circ}$ $\displaystyle Angle C = 20^{\circ}$

$Angle A = 44^{\circ}$ $\displaystyle Angle A = 44^{\circ}$

$Angle B = 32^{\circ}$ $\displaystyle Angle B = 32^{\circ}$

$Angle C = 104^{\circ}$ $\displaystyle Angle C = 104^{\circ}$

No solution

$Angle A = 114^{\circ}$ $\displaystyle Angle A = 114^{\circ}$

$Anbgle B = 32^{\circ}$ $\displaystyle Anbgle B = 32^{\circ}$

$Angle C = 36^{\circ}$ $\displaystyle Angle C = 36^{\circ}$

Correct answer:

$Angle A = 104^{\circ}$ $\displaystyle Angle A = 104^{\circ}$

$Angle B = 44^{\circ}$ $\displaystyle Angle B = 44^{\circ}$

$Angle C = 32^{\circ}$ $\displaystyle Angle C = 32^{\circ}$

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:

$\displaystyle 18x = 180$

x = 10 $\displaystyle x = 10$

Plug $\displaystyle x$ back into the three angle measurements:

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

$\displaystyle Angle A = 100 + 4$ 4

$\displaystyle Angle A = 104$

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

$\displaystyle Angle B = 50 -6$

$\displaystyle Angle B = 46$

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

$\displaystyle Angle C = 30 + 2$

$\displaystyle Angle C = 32$

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Example Question #491 : 2 Dimensional Geometry

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

Possible Answers:

$\displaystyle 31$

$\displaystyle 79$

$\displaystyle 11$

$\displaystyle 99$

$\displaystyle 89$

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: $\displaystyle 79$

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Example Question #5 : Supplementary Angles

What angle is supplementary to 54 degrees?

Possible Answers:

$\displaystyle 16$

126 $\displaystyle 126$

$\displaystyle 26$

116 $\displaystyle 116$

136 $\displaystyle 136$

Correct answer:

126 $\displaystyle 126$

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: 126 $\displaystyle 126$

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Example Question #3 : Supplementary Angles

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

Possible Answers:

$\displaystyle 64$

120 $\displaystyle 120$

160 $\displaystyle 160$

144 $\displaystyle 144$

$\displaystyle 18$

Correct answer:

144 $\displaystyle 144$

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.

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

x=18 $\displaystyle x=18$

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

The answer is: 144 $\displaystyle 144$

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Example Question #491 : Geometry And Graphs

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

Possible Answers:

$\displaystyle 60$

$\displaystyle 30$

$\displaystyle 61$

$\displaystyle 90$

180 $\displaystyle 180$

Correct answer:

180 $\displaystyle 180$

Explanation:

Supplementary angles sum to 180 degrees.

Set up an equation to solve for $\displaystyle x$.

$\displaystyle x+1+2x-1 = 180$

$\displaystyle 3x = 180$

x=60 $\displaystyle x=60$

Substitute this value to $\displaystyle 3x$.

$\displaystyle 3(60) = 180$

The answer is: 180 $\displaystyle 180$

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Example Question #61 : Angle Geometry

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

Possible Answers:

$\displaystyle 87$

2x-186 $\displaystyle 2x-186$

186-2x $\displaystyle 186-2x$

174-2x $\displaystyle 174-2x$

$\displaystyle 93$

Correct answer:

186-2x $\displaystyle 186-2x$

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: 186-2x $\displaystyle 186-2x$

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #56 : Complementary Angles

Example Question #51 : Angle Geometry

Example Question #2 : Supplementary Angles

Example Question #3 : Supplementary Angles

Example Question #4 : Supplementary Angles

Example Question #491 : 2 Dimensional Geometry

Example Question #5 : Supplementary Angles

Example Question #3 : Supplementary Angles

Example Question #491 : Geometry And Graphs

Example Question #61 : Angle Geometry

All GED Math Resources

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