Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #11 : Sectors

If you have \displaystyle 80\% of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

\displaystyle 280

\displaystyle 80

\displaystyle 108

\displaystyle 288

\displaystyle 308

Correct answer:

\displaystyle 288

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.

\displaystyle 80\% \rightarrow \frac{80}{100}=0.8

If you multiply 360 by 0.80, you get the degree measure that corresponds to the percentage, which is 288.

\displaystyle 360 \cdot 0.8= 288

Example Question #12 : Circles

If you have \displaystyle 44\% of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

\displaystyle 52.6

\displaystyle 44

\displaystyle 120

\displaystyle 158.4

\displaystyle 160.4

Correct answer:

\displaystyle 158.4

Explanation:

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

First convert the percentage into a decimal.

\displaystyle 44\% \rightarrow \frac{44}{100}=0.44

If you multiply 360 by 0.44, you get the degree measure that corresponds to the percentage, which is 158.4.

\displaystyle 360 \cdot 0.44=158.4

Example Question #13 : Circles

If you have \displaystyle 18\% of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

\displaystyle 68.4

\displaystyle 18

\displaystyle 64.8

\displaystyle 65

\displaystyle 70

Correct answer:

\displaystyle 64.8

Explanation:

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

First convert the percentage into a decimal.

\displaystyle 18\% \rightarrow \frac{18}{100}=0.18

If you multiply 360 by 0.18, you get the degree measure that corresponds to the percentage, which is 64.8.

\displaystyle 360 \cdot 0.18=64.8

Example Question #11 : Sectors

If you have \displaystyle 56\% of a circle, what is the angle, in degrees, that creates that region?

Possible Answers:

\displaystyle 270

\displaystyle 56

\displaystyle 200

\displaystyle 206.1

\displaystyle 201.6

Correct answer:

\displaystyle 201.6

Explanation:

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

We first need to convert the percentage into a decimal.

\displaystyle 56\% \rightarrow \frac{56}{100}=0.56

If you multiply 360 by 0.56, you get the degree measure that corresponds to the percentage, which is 201.6.

\displaystyle 360 \cdot 0.56=201.6

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

The central angle of a sector is 72o. What percentage of the circle is comprised by the sector?

Possible Answers:

\displaystyle 20\%

\displaystyle 80\%

\displaystyle 10\%

\displaystyle 40\%

Correct answer:

\displaystyle 20\%

Explanation:

The arc length of a sector, in degrees, is equal to the central angle. The total number of a degrees of a circle is 360. Therefore, we can use a proportion to calculate the percentage.

\displaystyle \frac{72}{360}=\frac{x}{100}

\displaystyle 7200=360x

\displaystyle 20=x

Therefore, 20% of the circle is comprised of the sector.

Example Question #2 : How To Find The Percentage Of A Sector From An Angle

A sector of a circle has a central angle of \displaystyle \small 135^\circ.  What percentage of the circle does the sector occupy?

Possible Answers:

\displaystyle \small 24\%

\displaystyle \small 75\%

\displaystyle \small 33\%

\displaystyle \small \small 37.5\%

\displaystyle \small 15\%

Correct answer:

\displaystyle \small \small 37.5\%

Explanation:

A whole circle is \displaystyle \small 360^\circ.  We therefore need to find the percent.  We can do this by dividing.

\displaystyle \small \frac{135}{360}=0.375=37.5\%

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

A survey was given to 250 high schoolers asking them how they got to school each day.  The sector representing the students that ride the bus is 100 degrees, the sector representing the students that drive their own car is 90 degrees, and the sector representing the students that walk or ride their bike is 85 degrees.  What percent of students get to school in another manner (parents drop them off, etc)?

Possible Answers:

\displaystyle 76.4\%

None of the other answers.

\displaystyle 2.4\%

\displaystyle 7.6\%

\displaystyle 23.6\%

Correct answer:

\displaystyle 23.6\%

Explanation:

To find the missing percentage, first you can add the 3 sectors' angle measures together to get 275 degrees.  

Then subtract that from 360 degrees because you want this missing sector, which is 85 degrees.  

Then set-up a proportion:

\displaystyle \frac{85}{360} = \frac{x}{100} and solve.

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

A circle graph is used to depict the results from a survey given to high school students regarding their favorite sport. The sector representing baseball measures 52 degrees.  What percent of the high schoolers who took the survey prefer baseball over any other sport?

Possible Answers:

\displaystyle 52\%

\displaystyle 14.4\%

None of the other answers.

\displaystyle 15\%

\displaystyle 1.44\%

Correct answer:

\displaystyle 14.4\%

Explanation:

To convert the angle of a sector in a circle to the percentage of that sector you can set-up a proportion: \displaystyle \frac{52}{360} = \frac{x}{100} and then solve.  The total number of degrees in a circle is 360, so you place 52 out of 360. The total percent being represented by a circle is 100, so you place \displaystyle x (what you are trying to find) out of 100.

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

A circle graph represents the different types of pie you can find at a local bakery. The blueberry pie wedge measures 120 degrees, the apple pie wedge measures 110 degrees and the cherry pie wedge measures 130 degrees.  What percent of pies in the bakery are either blueberry or cherry?

Possible Answers:

\displaystyle 69.4\%

\displaystyle 36.1\%

\displaystyle 33.3\%

\displaystyle 6.9\%

\displaystyle 30.6\%

Correct answer:

\displaystyle 69.4\%

Explanation:

First add together the degrees that represent blueberry and cherry pie to get 250 degrees.  You want to include both sectors because the question is asking for the percent of pies that is either blueberry or cherry.  

Then set up a proportion:

\displaystyle \frac{250}{360} = \frac{x}{100} and solve for \displaystyle x.

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

A circle graph represents the student population at a local high school.  The sector representing boys measures 200 degrees.  What percent of the high school is girls?

Possible Answers:

None of the other answers.

\displaystyle 4.4\%

\displaystyle 44.4\%

\displaystyle 5.6\%

\displaystyle 55.6\%

Correct answer:

\displaystyle 44.4\%

Explanation:

First subtract 200 from 360 to get the number of degrees making up the sector representing girls.  

Then set-up a proportion:

\displaystyle \frac{160}{360} = \frac{x}{100} and solve for \displaystyle x.

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