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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1 : Intermediate Geometry

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

Possible Answers:

$108^{\circ}$ $\displaystyle 108^{\circ}$

$126^{\circ}$ $\displaystyle 126^{\circ}$

$95^{\circ}$ $\displaystyle 95^{\circ}$

$75^{\circ}$ $\displaystyle 75^{\circ}$

$135^{\circ}$ $\displaystyle 135^{\circ}$

Correct answer:

$126^{\circ}$ $\displaystyle 126^{\circ}$

Explanation:

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

$x=0.35\cdot 360 = 126$ $\displaystyle x=0.35\cdot 360 = 126$

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

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

Possible Answers:

$\small 45^\circ$ $\displaystyle \small 45^\circ$

$\small 12.5^\circ$ $\displaystyle \small 12.5^\circ$

$\small 22.5^\circ$ $\displaystyle \small 22.5^\circ$

$\small 30^\circ$ $\displaystyle \small 30^\circ$

$\small 8^\circ$ $\displaystyle \small 8^\circ$

Correct answer:

$\small 45^\circ$ $\displaystyle \small 45^\circ$

Explanation:

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

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

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

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

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

Possible Answers:

240 $\displaystyle 240$

66.7% $\displaystyle 66.7%$

100 $\displaystyle 100$

210 $\displaystyle 210$

120 $\displaystyle 120$

Correct answer:

240 $\displaystyle 240$

Explanation:

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

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

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

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

$360 \cdot 0.667=240$ $\displaystyle 360 \cdot 0.667=240$

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

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

Possible Answers:

$\displaystyle 62$

$\displaystyle 72$

$\displaystyle 20$

$\displaystyle 18$

$\displaystyle 50$

Correct answer:

$\displaystyle 72$

Explanation:

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

First convert $20\%$ $\displaystyle 20\%$ into a decimal.

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

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

$360 \cdot 0.2=72$ $\displaystyle 360 \cdot 0.2=72$

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Example Question #3 : Plane Geometry

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

Possible Answers:

$\displaystyle 72$

$\displaystyle 30$

108 $\displaystyle 108$

100 $\displaystyle 100$

110 $\displaystyle 110$

Correct answer:

108 $\displaystyle 108$

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.

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

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

$360\cdot 0.3=108$ $\displaystyle 360\cdot 0.3=108$

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

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

Possible Answers:

120 $\displaystyle 120$

126 $\displaystyle 126$

$\displaystyle 35$

116 $\displaystyle 116$

130 $\displaystyle 130$

Correct answer:

126 $\displaystyle 126$

Explanation:

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

First convert the percent to decimal.

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

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

$360 \cdot 0.35=126$ $\displaystyle 360 \cdot 0.35=126$

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

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

Possible Answers:

330 $\displaystyle 330$

300 $\displaystyle 300$

344 $\displaystyle 344$

$\displaystyle 90$

324 $\displaystyle 324$

Correct answer:

324 $\displaystyle 324$

Explanation:

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

First convert the percentage into a decimal.

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

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

$360 \cdot 0.90=324$ $\displaystyle 360 \cdot 0.90=324$

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Example Question #1 : Circles

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

Possible Answers:

180 $\displaystyle 180$

170 $\displaystyle 170$

162 $\displaystyle 162$

$\displaystyle 45$

162 $\displaystyle 162$

Correct answer:

162 $\displaystyle 162$

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.

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

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

$360 \cdot 0.45=162$ $\displaystyle 360 \cdot 0.45=162$

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Example Question #1 : Circles

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

Possible Answers:

140 $\displaystyle 140$

37.5 $\displaystyle 37.5$

$\displaystyle 50$

135 $\displaystyle 135$

$\displaystyle 90$

Correct answer:

135 $\displaystyle 135$

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.

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

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

$360 \cdot 0.375=135$ $\displaystyle 360 \cdot 0.375=135$

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

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

Possible Answers:

280 $\displaystyle 280$

250 $\displaystyle 250$

252 $\displaystyle 252$

262 $\displaystyle 262$

$\displaystyle 70$

Correct answer:

252 $\displaystyle 252$

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.

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

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

$360 \cdot 0.7 =252$ $\displaystyle 360 \cdot 0.7 =252$

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : Intermediate Geometry

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 #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 : Circles

Example Question #1 : Circles

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

All Intermediate Geometry Resources

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