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Intermediate Geometry : How to find the angle of a sector

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Example Questions

Example Question #101 : Circles

A sector in a circle with a radius of has an area of $3\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$11^\circ$

$11.4^\circ$

$11.2^\circ$

$10.8^\circ$

Correct answer:

$10.8^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 3\pi}{\pi\times 10^2}=\frac{1080\pi}{100\pi}=10.8$

The central angle is 10.8 degrees.

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Example Question #111 : Circles

A sector in a circle with a radius of has an area of $8\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$15.50^\circ$

$10.50^\circ$

$11.25^\circ$

$9.75^\circ$

Correct answer:

$11.25^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 8\pi}{\pi\times 16^2}=\frac{2880\pi}{256\pi}=11.25$

The central angle is 11.25 degrees.

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Example Question #11 : How To Find The Angle Of A Sector

A sector in a circle with a radius of has a area of $50\pi$ . In degrees, what is the measurement of the central angle in the sector?

Possible Answers:

$42^\circ$

$39^\circ$

$45^\circ$

$36^\circ$

Correct answer:

$45^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 50\pi}{\pi\times 20^2}=\frac{18000\pi}{200\pi}=45$

The central angle is degrees.

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Example Question #112 : Sectors

A sector in a circle with a radius of has an area of $48\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$130^\circ$

$110^\circ$

$120^\circ$

$145^\circ$

Correct answer:

$120^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 48\pi}{\pi\times 12^2}=\frac{17280\pi}{144\pi}=120$

The central angle is 120 degrees.

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Example Question #112 : Circles

A sector in a circle with a radius of has an area of $\frac{1}{2}\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$80^\circ$

$10^\circ$

$40^\circ$

$20^\circ$

Correct answer:

$20^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times \frac{1}{2}\pi}{\pi\times 3^2}=\frac{180\pi}{9\pi}=20$

The central angle is degrees.

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Example Question #111 : Plane Geometry

A sector in a circle with a radius of has an area of $45\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$132.5^\circ$

$112.5^\circ$

$75.5^\circ$

$92.5^\circ$

Correct answer:

$112.5^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 45\pi}{\pi\times 12^2}=\frac{16200\pi}{144\pi}=112.5$

The central angle is 112.5 degrees.

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Example Question #115 : Sectors

A sector of a circle with a radius of has an area of $3\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$47.2^\circ$

$49.2^\circ$

$43.2^\circ$

$45.2^\circ$

Correct answer:

$43.2^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 3\pi}{\pi\times 5^2}=\frac{1080\pi}{25\pi}=43.2$

The central angle is 43.2 degrees.

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Example Question #112 : Plane Geometry

A sector in a circle with a radius of has an area of $\frac{1}{4}\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$8.555^\circ$

$6.225^\circ$

$2.775^\circ$

$5.625^\circ$

Correct answer:

$5.625^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times \frac{1}{4}\pi}{\pi\times 4^2}=\frac{90\pi}{16\pi}=5.625$

The central angle is 5.625 degrees.

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Example Question #117 : Sectors

A sector in a circle with a radius of has an area of $14\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$140^\circ$

$150^\circ$

$130^\circ$

$120^\circ$

Correct answer:

$140^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 14\pi}{\pi\times 6^2}=\frac{5040\pi}{36\pi}=140$

The central angle is 140 degrees.

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Example Question #113 : Plane Geometry

A sector in a circle with a radius of has an area of $35\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$340^\circ$

$320^\circ$

$330^\circ$

$350^\circ$

Correct answer:

$350^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 35\pi}{\pi\times 6^2}=\frac{12600\pi}{36\pi}=350$

The central angle is 350 degrees.

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Intermediate Geometry : How to find the angle of a sector

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #101 : Circles

Example Question #111 : Circles

Example Question #11 : How To Find The Angle Of A Sector

Example Question #112 : Sectors

Example Question #112 : Circles

Example Question #111 : Plane Geometry

Example Question #115 : Sectors

Example Question #112 : Plane Geometry

Example Question #117 : Sectors

Example Question #113 : Plane Geometry

All Intermediate Geometry Resources

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