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GED Math : GED Math

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Example Questions

Example Question #2 : Angles

Pentagon

Note: Figure NOT drawn to scale.

Refer to the above figure. $\Delta OKR$ is equilateral and Pentagon KLMNO is regular.

Evaluate $m \angle NRO$ .

Possible Answers:

$66^{\circ }$

$48^{\circ }$

$54 ^{\circ }$

$72^{\circ }$

Correct answer:

$66^{\circ }$

Explanation:

First, we find $m \angle NOR$ .

By angle addition,

$m \angle NOR + m \angle ROK = m \angle NOK$ .

$\angle NOK$ is an angle of a regular pentagon and has measure $\frac{180^{\circ}\times (5-2)}{5} = 108 ^{\circ}$ .

$\angle ROK$ , as an angle of an equilateral triangle, has measure $60 ^{\circ }$ .

$m \angle NOR + 60 ^{\circ }= 108 ^{\circ }$

$m \angle NOR = 48 ^{\circ }$

$\Delta OKR$ is equilateral, so $\overline{OR} \cong \overline{OK}$ ; Pentagon KLMNO is regular, so $\overline{OK} \cong \overline{NO}$ . Therefore, $\overline{OR} \cong \overline{ON}$ , and by the Isosceles Triangle Theorem, $m \angle NRO = m \angle RNO$ .

The degree measures of three angles of a triangle total $180 ^{\circ }$ , so:

$m \angle NRO + m \angle RNO + m \angle NOR = 180^{\circ }$

$m \angle NRO + m \angle NRO + 48^{\circ } = 180^{\circ }$

$2 m \angle NRO + 48^{\circ } = 180^{\circ }$

$2 m \angle NRO = 132^{\circ }$

$m \angle NRO = 66^{\circ }$

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Example Question #1391 : Ged Math

Pentagon_1

Refer to the above figure, which shows Square OPQK and regular Pentagon KLMNO .

Evaluate $m \angle NOQ$ .

Possible Answers:

$135^{\circ}$

$168^{\circ}$

$165^{\circ}$

$153^{\circ}$

Correct answer:

$153^{\circ}$

Explanation:

By angle addition,

$m \angle NOQ = m \angle NOK + m \angle KOQ$ .

$\angle NOK$ is an angle of a regular pentagon and has measure $\frac{180^{\circ}\times (5-2)}{5} = 108 ^{\circ}$ .

$\angle KOQ$ is one of two acute angles of isosceles right triangle $\Delta KOQ$ , so $m \angle KOQ = 45^{\circ }$ .

$m \angle NOQ = 108^{\circ } + 45^{\circ } = 153^{\circ }$

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Example Question #1392 : Ged Math

Thingy_2

Refer to the above figure. $\Delta OKR$ is equilateral, and Quadrilateral OPQK is a square.

Evaluate $m \angle ROP$ .

Possible Answers:

$135^{\circ }$

$150 ^{\circ }$

$168^{ \circ }$

$140 ^{\circ }$

Correct answer:

$150 ^{\circ }$

Explanation:

By angle addition,

$m \angle ROP = m \angle ROK + m \angle KOP$ .

$\angle ROK$ , as an angle of an equilateral triangle, has measure $60 ^{\circ }$ .

$\angle KOP$ , as an angle of a square, has measure $90 ^{\circ }$ .

Therefore,

$m \angle ROP = 60 ^{\circ } + 90^{\circ } = 150 ^{\circ }$ .

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Example Question #2 : Angles

Give the number of sides of a regular polygon whose interior angles have measure $170^{\circ }$ .

Possible Answers:

Correct answer:

Explanation:

The easiest way to solve this is to look at the exterior angles, each of which have measure $(180-170)^{\circ } = 10^{\circ }$ . Since each exterior angle of a regular polygon with sides is $\frac{360}{N}$ , we solve for in the following equation:

$\frac{360}{N} = 10$

$\frac{360}{N} \cdot \frac{N }{10} = 10 \cdot \frac{N }{10}$

36 = N

The polygon has 36 sides.

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Example Question #423 : 2 Dimensional Geometry

Three consecutive even angles add up to 180 . What must be the value of the second largest angle?

Possible Answers:

Correct answer:

Explanation:

Let be an even angle. The next consecutive even values are x+2, x+4 .

Set up an equation such that all angles added equal to 180.

x+(x+2)+(x+4) = 180

3x+6 = 180

3x=174

Divide by three on both sides.

$\frac{3x}{3}=\frac{174}{3}$

x=58

The second largest angle is x+2 .

Substitute the value of in to the expression.

58+2 = 60

The answer is:

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Example Question #1391 : Ged Math

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 $\angle GFE$

$\angle EFC$ and $\angle FCD$

$\angle AFC$ and $\angle EFG$

$\angle ECD$ and $\angle DEC$

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 #1392 : Ged Math

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 = 5

x = 17

x = 29

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 #1393 : Ged Math

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

Possible Answers:

144^o

18^o

108^o

72^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 #2 : 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 = -8

x = 17

x = 5

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 #1 : 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:

$Angle A = 10^{\circ}$

$Angle B = 80^{\circ}$

No solution

$Angle A = 14^{\circ}$

$Angle B = 76^{\circ}$

$Angle A = 20^{\circ}$

$Angle B = 70^{\circ}$

$Angle A = 15^{\circ}$

$Angle B = 75^{\circ}$

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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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #2 : Angles

Example Question #1391 : Ged Math

Example Question #1392 : Ged Math

Example Question #2 : Angles

Example Question #423 : 2 Dimensional Geometry

Example Question #1391 : Ged Math

Example Question #1392 : Ged Math

Example Question #1393 : Ged Math

Example Question #2 : Complementary Angles

Example Question #1 : Complementary Angles

All GED Math Resources

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