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GED Math : 2-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #51 : Complementary Angles

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

$m\angle A=18^{o}$

Possible Answers:

$m\angle B=82^{o}$

$m\angle B=36^{o}$

$m\angle B=136^{o}$

$m\angle B=72^{o}$

Correct answer:

$m\angle B=72^{o}$

Explanation:

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:

$m\angle B=90^{o}-18^{o}=72^{o}$

This gives us a final answer of 72 degrees for angle B.

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Example Question #52 : Complementary Angles

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

$m\angle A=87^{o}$

Possible Answers:

$m\angle B=3^{o}$

$m\angle B=72^{o}$

$m\angle B=112^{o}$

$m\angle B=13^{o}$

Correct answer:

$m\angle B=3^{o}$

Explanation:

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:

$m\angle B=90^{o}-87^{o}=3^{o}$

This gives us a final answer of 3 degrees for angle B.

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Example Question #53 : Complementary Angles

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

$m\angle A=39^{o}$

Possible Answers:

$m\angle B=123^{o}$

$m\angle B=3^{o}$

$m\angle B=11^{o}$

$m\angle B=51^{o}$

Correct answer:

$m\angle B=51^{o}$

Explanation:

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:

$m\angle B=90^{o}-39^{o}=51^{o}$

This gives us a final answer of 51 degrees for angle B.

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Example Question #54 : Complementary Angles

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

$m\angle A=53^{o}$

Possible Answers:

$m\angle B=37^{o}$

$m\angle B=116^{o}$

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

$m\angle B=11^{o}$

Correct answer:

$m\angle B=37^{o}$

Explanation:

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:

$m\angle B=90^{o}-53^{o}=37^{o}$

This gives us a final answer of 37 degrees for angle B.

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Example Question #55 : Complementary Angles

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

$m\angle A=9^{o}$

Possible Answers:

$m\angle B=12^{o}$

$m\angle B=85^{o}$

$m\angle B=116^{o}$

$m\angle B=81^{o}$

Correct answer:

$m\angle B=81^{o}$

Explanation:

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:

$m\angle B=90^{o}-9^{o}=81^{o}$

This gives us a final answer of 81 degrees for angle B.

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Example Question #56 : Angle Geometry

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

Possible Answers:

66.5

65.5

75.5

67.5

Correct answer:

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 , and the given angle is 23.5 .

So, we will subtract 23.5 from .

Other angle= 90-23.5=66.5

The other angle has a measurement of 66.5 degrees.

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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 #487 : 2 Dimensional Geometry

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 = 24

x = 16

x = -2

x = 10

x= 14

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 #488 : 2 Dimensional Geometry

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 = -10

No solution

x = 10

x = 5

x = 15

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 #489 : 2 Dimensional Geometry

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:

$Angle A = 44^{\circ}$

$Angle B = 32^{\circ}$

$Angle C = 104^{\circ}$

$Angle A = 120^{\circ}$

$Angle B = 40^{\circ}$

$Angle C = 20^{\circ}$

No solution

$Angle A = 104^{\circ}$

$Angle B = 44^{\circ}$

$Angle C = 32^{\circ}$

$Angle A = 114^{\circ}$

$Anbgle B = 32^{\circ}$

$Angle C = 36^{\circ}$

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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GED Math : 2-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #51 : Complementary Angles

Example Question #52 : Complementary Angles

Example Question #53 : Complementary Angles

Example Question #54 : Complementary Angles

Example Question #55 : Complementary Angles

Example Question #56 : Angle Geometry

Example Question #1 : Supplementary Angles

Example Question #487 : 2 Dimensional Geometry

Example Question #488 : 2 Dimensional Geometry

Example Question #489 : 2 Dimensional Geometry

All GED Math Resources

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