ACT Math : How to find the angle for a percentage of a circle

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

Generalsector

The sector pictured above is  of the circle. What is the angle measure  for the sector?

Possible Answers:

Correct answer:

Explanation:

A question like this is very easy. You merely need to find out what is  of the total  degrees in a circle. This is:

. That is it!

Example Question #1 : Sectors

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The area of sector  is . This figure is not drawn to scale.

What is the measure of the angle of the sector?

Possible Answers:

Correct answer:

Explanation:

You know that the area of a circle is computed by the equation:

For our data, this is:

 or 

Now, the sector is a percentage of the circle. For the areas, this can be represented as the fraction:

The total degree measure of a circle is, of course,  degrees.  This means that the sector contains:

.

Example Question #1 : Sectors

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The arc length of sector above is . This figure is not drawn to scale.

What is the angle measure of sector ?

Possible Answers:

Correct answer:

Explanation:

You know that the circumference of a circle is computed by the equation:

For our data, this is:

Now, the sector is a percentage of the circle. For the lengths of the circumference and the arc length, this can be represented as the fraction:

The total degree measure of a circle is, of course,  degrees. This means that the sector contains:

.

Example Question #4 : How To Find The Angle For A Percentage Of A Circle

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Sector  is  of the total circle. This figure is not drawn to scale.

What is the angle of this sector?

Possible Answers:

Correct answer:

Explanation:

Do not overthink this question! All you need to remember is that a given circle contains  degrees. This means that the sector is merely a percentage of . For our question, this percentage is , which is the same as . So, to calculate, you merely need to multiply:

This is the degree measure of the sector.

Example Question #2 : Sectors

A bike wheel has  evenly spaced spokes spreading from its center to its tire. What must the angle be for the spokes in order to guarantee this even spacing? Round to the nearest hundredth.

Possible Answers:

Correct answer:

Explanation:

Remember that the total degree measure of a circle is . This means that if you have  parts into which you have divided your circle, each spoke must be  or  apart.

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