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GED Math : Geometry and Graphs

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Example Questions

Example Question #11 : Supplementary Angles

There are three angles that, altogether, are supplementary. The second angle is 10 degrees larger than the first, while the third is 10 larger than the second. What is the size of the middle-sized angle?

Possible Answers:

$50^\circ$

$60^\circ$

$80^\circ$

$75^\circ$

Cannot be computed from the information provided

Correct answer:

$60^\circ$

Explanation:

Since all three angles are supplementary, you know that they must add up to 180 degrees. However, you need to manage some of the other details. Imagine that the first one is degrees. The second must be d+10 degrees. This means that the third is (d+10)+10 or d+20 degrees. Therefore, you could draw the following:

Comp4

Based on this data, you know:

d+d+10+d+20=180

Simplifying, you get:

3d+30=180

3d=150

d=50

The middle angle is d+10 or 50+10=60 degrees

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Example Question #502 : 2 Dimensional Geometry

Angles x and y are supplementary. If $y = 45$^{\circ}$$ , what is the value of x?

Possible Answers:

$45$^{\circ}$$

$65$^{\circ}$$

$180$^{\circ}$$

$315$^{\circ}$$

$135$^{\circ}$$

Correct answer:

$135$^{\circ}$$

Explanation:

Two angles are supplementary if they add up to $180$^{\circ}$$ . So, to find supplementary angles, we will use the following formula:

$\text{angle } x + \text{ angle } y = 180$^{\circ}$$

Now, we know $y= 45$^{\circ}$$ . So, we can substitute and solve for x. We get

$x + 45$^{\circ}$ = 180$^{\circ}$$

$x + 45$^{\circ}$ - 45$^{\circ}$ = 180$^{\circ}$ - 45$^{\circ}$$

$x+ 0$^{\circ}$ = 135$^{\circ}$$

$x = 135$^{\circ}$$

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Example Question #12 : Supplementary Angles

Suppose a pair of angles are supplementary. What is the other angle if one angle is 180x-90 ?

Possible Answers:

270-180x

180x-270

90-180x

180x-90

-180x-90

Correct answer:

270-180x

Explanation:

Supplementary angles add up to 180 degrees.

To find the other angle, we will need to subtract the given angle from 180.

180-(180x-90) = 180-180x+90

Combine like-terms.

The answer is: 270-180x

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Example Question #504 : 2 Dimensional Geometry

Angles x and y are supplementary. If $y=45^{\circ}$ , find x.

Possible Answers:

$x=110^{\circ}$

$x=135^{\circ}$

$x=25^{\circ}$

$x=45^{\circ}$

$x=315^{\circ}$

Correct answer:

$x=135^{\circ}$

Explanation:

Two angles are supplementary if they add up to $180^{\circ}$ . So, we use the following formula:

$x+y=180^{\circ}$

Now, we know $y=45^{\circ}$ So, we will substitute and solve for x. We get

$x+45^{\circ}=180^{\circ}$

$x+45^{\circ}-45^{\circ}=180^{\circ}-45^{\circ}$

$x+0^{\circ}=135^{\circ}$

$x=135^{\circ}$

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Example Question #505 : 2 Dimensional Geometry

If two angles are supplementary, where one given angle measurement is 90x +30 degrees, and the other angle is 10x+20 degrees,what must be the value of ?

Possible Answers:

$\textup{Cannot be determined.}$

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{13}{10}$

$\frac{13}{20}$

Correct answer:

$\frac{13}{10}$

Explanation:

Set up an equation such that both angles will add up to 180 degrees, since these are supplementary angles.

90x+30+10x+20 = 180

Combine like-terms.

100x+50 = 180

Subtract fifty from both sides.

100x+50 -50= 180-50

100x=130

Divide by 100 on both sides.

$\frac{100x}{100}=\frac{130}{100}$

The answer is: $\frac{13}{10}$

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Example Question #506 : 2 Dimensional Geometry

Angles

Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

Possible Answers:

x = 36

x = 51

x = 41

x = 46

Correct answer:

x = 46

Explanation:

The marked angles form a linear pair and are therefore supplementary - their degree measures total $180^{\circ }$ . Set the sum of the expressions equal to 180, and solve for :

x + (x+88) = 180

Simplify and collect like terms:

x+x + 88 = 180

2x+88 = 180

Subtract 88 from both sides:

2x+88 - 88 = 180 - 88

2x = 92

Divide both sides by 2:

$\frac{2x }{2}= \frac{92}{2}$

x = 46

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Example Question #501 : Geometry And Graphs

If an angle is measured 75 degrees, what is the other angle if both angles are supplementary?

Possible Answers:

115

105

125

165

Correct answer:

105

Explanation:

Supplementary angles sum up to 180 degrees.

To find the other angle, subtract the given angle from 180 degrees.

180-75= 105

The answer is: 105

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Example Question #22 : Supplementary Angles

Suppose the angle and are supplementary. What must be a possible angle?

Possible Answers:

108

120

144

Correct answer:

144

Explanation:

If two angles are supplementary, they must add up to 180 degrees.

Set up an equation such that both angles will add to 180 degrees.

x+4x = 180

Solve the equation.

5x =180

Divide by 5 on both sides.

$\frac{5x }{5}=\frac{180}{5}$

x=36

4x = 4(36) = 144

One of the possible angles is either or 144 .

The answer is: 144

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Example Question #502 : Geometry And Graphs

Two angles are supplementary if they add up to:

Possible Answers:

$45^{\circ}$

$90^{\circ}$

$360^{\circ}$

$180^{\circ}$

$225^{\circ}$

Correct answer:

$180^{\circ}$

Explanation:

Two angles are supplementary if they add up to $180^{\circ}$ .

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Example Question #24 : Supplementary Angles

Two angles are supplementary. If one angle is $112^{\circ}$ , what is the value of the other angle?

Possible Answers:

$248^{\circ}$

$113^{\circ}$

$22^{\circ}$

$67^{\circ}$

$68^{\circ}$

Correct answer:

$68^{\circ}$

Explanation:

If two angles are supplementary, they add up to $180^{\circ}$ . So, we can use the formula:

$x+y = 180^{\circ}$

Now, we know one angle is $112^{\circ}$ . So, we can substitute and then solve for the other angle. So, we get

$112^{\circ} + y = 180^{\circ}$

$112^{\circ} - 112^{\circ} + y = 180^{\circ} - 112^{\circ}$

$0^{\circ}+y=68^{\circ}$

$y = 68^{\circ}$

Therefore, the other angle is $68^{\circ}$ .

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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 #11 : Supplementary Angles

Example Question #502 : 2 Dimensional Geometry

Example Question #12 : Supplementary Angles

Example Question #504 : 2 Dimensional Geometry

Example Question #505 : 2 Dimensional Geometry

Example Question #506 : 2 Dimensional Geometry

Example Question #501 : Geometry And Graphs

Example Question #22 : Supplementary Angles

Example Question #502 : Geometry And Graphs

Example Question #24 : Supplementary Angles

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