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GED Math : Geometry and Graphs

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Example Questions

Example Question #1 : Angle Geometry

Thingy

Refer to the above figure. You are given that $\overleftrightarrow{AE} ||\overleftrightarrow{BD}$ .

Which two angles must be complementary?

Possible Answers:

$\angle AFG$ and $\angle GFE$

$\angle ECD$ and $\angle DEC$

$\angle EFC$ and $\angle FCD$

$\angle AFC$ and $\angle EFG$

Correct answer:

$\angle ECD$ and $\angle DEC$

Explanation:

$\angle AFG$ and $\angle GFE$ form a linear pair, so their measures add up to that of a straight angle, which is $180^{\circ }$ . They must be supplementary (and cannot be complementary).

$\angle AFC$ and $\angle EFG$ are a pair of vertical angles - angles formed from a pair of intersecting lines which together have the lines as the union. They must be congruent, and need not be complementary.

$\angle EFC$ and $\angle FCD$ are a pair of same-side interior angles formed by transversal $\overleftrightarrow{FC}$ across the parallel lines. They must be supplementary (and cannot be complementary).

$\angle ECD$ and $\angle DEC$ are the acute angles of right triangle $\Delta DEC$ . They must be complementary. This is the correct pair.

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Example Question #2 : Angle Geometry

Angles A and B are complementary angles. The measure of angle A is 5x - 17 , The measure of Angle B is 3x - 29 . find the value of .

Possible Answers:

x = 17

x = 29

x = 5

x = -17

x = 10

Correct answer:

x = 17

Explanation:

Since angles A and B are complementary, their measures add up to 90 degrees. Therefore we can set up our equation as such:

A + B = 90

-or-

5x - 17 + 3x - 29 = 90

Combine like terms and solve for :

8x - 46 = 90

8x = 136

x = 17

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Example Question #3 : Angle Geometry

What is the measure of an angle that is complementary to an angle measuring 72^o ?

Possible Answers:

108^o

18^o

72^o

144^o

Correct answer:

18^o

Explanation:

The sum of complementary angles is equal to 90^o .

Set up the following equation and solve for :

72+x=90

72-72+x=90-72

x=18

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Example Question #4 : Complementary Angles

Angles A and B are complementary angles. The measure of angle A is 4x + 25 . The measure of angle B is 6x - 15 . Solve for .

Possible Answers:

x = -8

x = -5

x = 5

x = 8

x = 17

Correct answer:

x = 8

Explanation:

Since angles A and B are complementary angles, their measurements add up to equal 90. Therefore, we need to set up our equation as follows:

A + B = 90

-or-

4x + 25 + 6x - 15 = 90

Combine like terms:

10x + 10 = 90

And solve for :

10x = 80

x = 8

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Example Question #4 : Complementary Angles

Angles A and B are complementary angles. The measure of angle A is -2x + 50 . The measure of angle B is 5x - 20 . What are the measures of the two angles?

Possible Answers:

$Angle A = 14^{\circ}$

$Angle B = 76^{\circ}$

$Angle A = 10^{\circ}$

$Angle B = 80^{\circ}$

$Angle A = 15^{\circ}$

$Angle B = 75^{\circ}$

$Angle A = 20^{\circ}$

$Angle B = 70^{\circ}$

No solution

Correct answer:

$Angle A = 10^{\circ}$

$Angle B = 80^{\circ}$

Explanation:

Since angles A and B are complementary, their measures add up to equal 90 degrees. Therefore we can set up an equation as follows:

A + B = 90

-or-

-2x + 50 + 5x - 20 = 90

Combine like terms and solve for :

3x + 30 = 90

3x = 60

x = 20

Now that we have found , we need to plug that back in to the two angle measurements

Angle A = -2(20) + 50

Angle A = -40 + 50

Angle A = 10

Angle B = 5(20) -20

Angle B = 100 - 20

Angle B = 80

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Example Question #3 : Complementary Angles

What angle is complementary to 55?

Possible Answers:

135

125

Correct answer:

Explanation:

The definition of a complementary angle means that two angles must add up to 90 degrees.

To find the angle, simply subtract 55 from 90.

90-55 = 35

The answer is:

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Example Question #5 : Complementary Angles

What angle is complementary to 10 degrees?

Possible Answers:

110

190

170

Correct answer:

Explanation:

Complementary angles must add up to ninety.

Subtract the given angle from 90 to find the other angle.

90-10 = 80

The answer is:

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Example Question #5 : Angle Geometry

Suppose the angles (3x+2) and (5x-7) are complementary angles. What is the value of ?

Possible Answers:

$\frac{99}{4}$

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

$\frac{95}{4}$

$\frac{99}{8}$

Correct answer:

$\frac{95}{4}$

Explanation:

Set up the equation such that both angles sum up to 90.

(3x+2)+ (5x-7) = 90

8x -5 = 90

Add 5 on both sides.

8x -5 +5= 90+5

8x=95

Divide both sides by 8.

$\frac{8x}{8}=\frac{95}{8}$

The value of is: $2(\frac{95}{8}) = \frac{95}{4}$

The answer is: $\frac{95}{4}$

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Example Question #6 : Angle Geometry

Determine the value of if the angles (x+2) and (x+6) are complementary.

Possible Answers:

Correct answer:

Explanation:

Complementary angles must add up to 90 degrees.

Set up an equation so that the sum of two angles add up to 90.

(x+2)+(x+6) = 90

2x+8 = 90

Subtract 8 on both sides.

2x+8 -8= 90-8

Simplify both sides.

2x = 82

Divide by two on both sides.

$\frac{2x }{2}= \frac{82}{2}$

x=41

The answer is:

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Example Question #8 : Angle Geometry

What angle is complementary to $\frac{\pi}{3}$ radians?

Possible Answers:

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

$\frac{\pi}{4}$

$\frac{\pi}{8}$

$\frac{\pi}{6}$

$\frac{\pi}{12}$

Correct answer:

$\frac{\pi}{6}$

Explanation:

Note that this is in radians. Recall that 2 complementary angles must add up to 90 degrees.

Since $\pi\textup{ radians} = 180 \textup{ degrees}$ ,

$\frac{\pi}{2}\textup{ radians} = 90 \textup{ degrees}$

To find the complementary angle, subtract $\frac{\pi}{3}$ from $\frac{\pi}{2}$ .

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

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

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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Angle Geometry

Example Question #2 : Angle Geometry

Example Question #3 : Angle Geometry

Example Question #4 : Complementary Angles

Example Question #4 : Complementary Angles

Example Question #3 : Complementary Angles

Example Question #5 : Complementary Angles

Example Question #5 : Angle Geometry

Example Question #6 : Angle Geometry

Example Question #8 : Angle Geometry

All GED Math Resources

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