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Intermediate Geometry : How to find the angle for a percentage of a circle

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Example Questions

Example Question #1 : How To Find The Angle For A Percentage Of A Circle

How many degrees are in $35\%$ of a circle?

Possible Answers:

$135^{\circ}$

$95^{\circ}$

$75^{\circ}$

$108^{\circ}$

$126^{\circ}$

Correct answer:

$126^{\circ}$

Explanation:

There are 360 degrees in a circleso the equation to solve becomes a simple percentage problem:

$x=0.35\cdot 360 = 126$

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Example Question #1 : Circles

A sector contains $\small 12.5\%$ of a circle. What is the measure of the central angle of the sector?

Possible Answers:

$\small 12.5^\circ$

$\small 45^\circ$

$\small 8^\circ$

$\small 30^\circ$

$\small 22.5^\circ$

Correct answer:

$\small 45^\circ$

Explanation:

An entire circle is $\small 360^\circ$ . A sector that is $\small 12.5\%$ of the circle therefore has a central angle that is $\small 12.5\%$ of $\small 360^\circ$ .

$\small 12.5\%(360)=45$

Therefore, our central angle is $\small 45^\circ$

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Example Question #1 : How To Find The Angle For A Percentage Of A Circle

If you have 66.7 percent of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

240

100

66.7%

120

210

Correct answer:

240

Explanation:

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

Now you need to convert $66.7\%$ into a decimal.

$66.7\% \rightarrow \frac{66.7}{100}=0.667$

If you multiply 360 by 0.667, you get the degree measure that corresponds to the percentage, which is 240.

$360 \cdot 0.667=240$

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Example Question #1 : How To Find The Angle For A Percentage Of A Circle

If you have $20\%$ of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

Correct answer:

Explanation:

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First convert $20\%$ into a decimal.

$20\% \rightarrow \frac{20}{100}=0.2$

If you multiply 360 by 0.20, you get the degree measure that corresponds to the percentage, which is 72.

$360 \cdot 0.2=72$

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Example Question #3 : Plane Geometry

If you have $30\%$ of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

108

100

110

Correct answer:

108

Explanation:

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

In order to start this problem we need to convert the percent into a decimal.

$30\% \rightarrow \frac{30}{100}=0.3$

If you multiply 360 by 0.30, you get the degree measure that corresponds to the percentage, which is 108.

$360\cdot 0.3=108$

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Example Question #1 : How To Find The Angle For A Percentage Of A Circle

If you have $35\%$ of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

116

120

126

130

Correct answer:

126

Explanation:

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First convert the percent to decimal.

$35\% \rightarrow \frac{35}{100}=0.35$

Now if you multiply 360 by 0.35, you get the degree measure that corresponds to the percentage, which is 126.

$360 \cdot 0.35=126$

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Example Question #7 : How To Find The Angle For A Percentage Of A Circle

If you have $90\%$ of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

330

300

344

324

Correct answer:

324

Explanation:

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First convert the percentage into a decimal.

$90\% \rightarrow \frac{90}{100}=0.9$

If you multiply 360 by 0.90, you get the degree measure that corresponds to the percentage, which is 324.

$360 \cdot 0.90=324$

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Example Question #1 : How To Find The Angle For A Percentage Of A Circle

If you have $45\%$ of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

162

180

162

170

Correct answer:

162

Explanation:

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First we need to convert the percentage into a decimal.

$45\% \rightarrow \frac{45}{100}=0.45$

If you multiply 360 by 0.45, you get the degree measure that corresponds to the percentage, which is 162.

$360 \cdot 0.45=162$

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Example Question #2 : How To Find The Angle For A Percentage Of A Circle

If you have $37.5\%$ of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

37.5

140

135

Correct answer:

135

Explanation:

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

In order to solve this problem we first need to convert the percentage into a decimal.

$37.5\% \rightarrow \frac{37.5}{100}=0.375$

If you multiply 360 by 0.375, you get the degree measure that corresponds to the percentage, which is 135.

$360 \cdot 0.375=135$

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Example Question #1 : How To Find The Angle For A Percentage Of A Circle

If you have $70\%$ of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

280

250

252

262

Correct answer:

252

Explanation:

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First we need to convert the percentage into a decimal.

$70\% \rightarrow \frac{70}{100}=0.7$

If you multiply 360 by 0.70, you get the degree measure that corresponds to the percentage, which is 252.

$360 \cdot 0.7 =252$

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Intermediate Geometry : How to find the angle for a percentage of a circle

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Angle For A Percentage Of A Circle

Example Question #1 : Circles

Example Question #1 : How To Find The Angle For A Percentage Of A Circle

Example Question #1 : How To Find The Angle For A Percentage Of A Circle

Example Question #3 : Plane Geometry

Example Question #1 : How To Find The Angle For A Percentage Of A Circle

Example Question #7 : How To Find The Angle For A Percentage Of A Circle

Example Question #1 : How To Find The Angle For A Percentage Of A Circle

Example Question #2 : How To Find The Angle For A Percentage Of A Circle

Example Question #1 : How To Find The Angle For A Percentage Of A Circle

All Intermediate Geometry Resources

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