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ACT Math : 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

Generalsector

The sector pictured above is $45\%$ of the circle. What is the angle measure for the sector?

Possible Answers:

$81^{\circ}$

$162^{\circ}$

$90^{\circ}$

$135.5^{\circ}$

$121.5^{\circ}$

Correct answer:

$162^{\circ}$

Explanation:

A question like this is very easy. You merely need to find out what is $45\%$ of the total 360 degrees in a circle. This is:

$0.45 * 360 =162^{\circ}$ . That is it!

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Example Question #1 : Sectors

_arc3

The area of sector ABC is $80\pi\:cm^2$ . This figure is not drawn to scale.

What is the measure of the angle of the sector?

Possible Answers:

$\frac{1}{12}^{\circ}$

$\frac{1}{20}^{\circ}$

$40^{\circ}$

$18^{\circ}$

$12^{\circ}$

Correct answer:

$18^{\circ}$

Explanation:

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

$A=\pi r^2$

For our data, this is:

$A=\pi 40^2$ or $A=1600\pi\:cm^2$

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

$\frac{80\pi\:cm^2}{1600\pi\:cm^2}=\frac{1}{20}$

The total degree measure of a circle is, of course, 360 degrees. This means that the sector contains:

$360^{\circ} * \frac{1}{20}=18^{\circ}$ .

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Example Question #2 : Sectors

_arc5

The arc length of sector above is $4\pi\:in$ . This figure is not drawn to scale.

What is the angle measure of sector ABC ?

Possible Answers:

$45^{\circ}$

$16\pi^{\circ}$

$90^{\circ}$

$75^{\circ}$

$\frac{1}{4}^{\circ}$

Correct answer:

$90^{\circ}$

Explanation:

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

$C=2\pi r$

For our data, this is:

$C=2*8\pi=16\pi\:in$

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:

$\frac{4\pi\:in}{16\pi\:in}=\frac{1}{4}$

The total degree measure of a circle is, of course, 360 degrees. This means that the sector contains:

$360^{\circ} * \frac{1}{4}=90^{\circ}$ .

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

_arc2

Sector ABC is $34\%$ of the total circle. This figure is not drawn to scale.

What is the angle of this sector?

Possible Answers:

$112^{\circ}$

$61.2^{\circ}$

$68^{\circ}$

$122.4^{\circ}$

$14^{\circ}$

Correct answer:

$122.4^{\circ}$

Explanation:

Do not overthink this question! All you need to remember is that a given circle contains 360 degrees. This means that the sector is merely a percentage of 360 . For our question, this percentage is , which is the same as 0.34 . So, to calculate, you merely need to multiply:

$0.34 * 360^{\circ} = 122.4^{\circ}$

This is the degree measure of the sector.

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Example Question #5 : 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:

$24$^{\circ}$$

$35.2$^{\circ}$$

$13.33$^{\circ}$$

$6.67$^{\circ}$$

$48$^{\circ}$$

Correct answer:

$24$^{\circ}$$

Explanation:

Remember that the total degree measure of a circle is $360$^{\circ}$$ . This means that if you have parts into which you have divided your circle, each spoke must be $\frac{360}{15}$ or $24$^{\circ}$$ apart.

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

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #1 : Sectors

Example Question #2 : Sectors

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

Example Question #5 : Sectors

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