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

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #1 : Plane Geometry

How many degrees are in of a circle?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #1 : Circles

A sector contains  of a circle.  What is the measure of the central angle of the sector?

Possible Answers:

Correct answer:

Explanation:

An entire circle is . A sector that is  of the circle therefore has a central angle that is  of .

Therefore, our central angle is 

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

If you have  percent 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.

Now you need to convert  into a decimal.

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

Example Question #3 : Circles

If you have  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  into a decimal.

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

Example Question #4 : Circles

If you have  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.

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

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

Example Question #5 : Circles

If you have  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 the percent to decimal.

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

Example Question #6 : Circles

If you have  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 the percentage into a decimal.

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

Example Question #7 : Circles

If you have  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 we need to convert the percentage into a decimal.

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

Example Question #9 : Plane Geometry

If you have  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.

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

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

Example Question #8 : Circles

If you have  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 we need to convert the percentage into a decimal.

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

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