ISEE Upper Level Quantitative : How to find the angle for a percentage of a circle

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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Example Questions

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

Generalsector

What is the angle measure of \(\displaystyle x\) in the figure above if the sector comprises 37% of the circle?

Possible Answers:

\(\displaystyle 78.4\)˚

\(\displaystyle 66.6\)˚

\(\displaystyle 121.3\)˚

\(\displaystyle 133.2\)˚

\(\displaystyle 37\)˚

Correct answer:

\(\displaystyle 133.2\)˚

Explanation:

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle.  To do this, you merely need to multiply \(\displaystyle 0.37\) by \(\displaystyle 360\)˚.  This yields \(\displaystyle 133.2\)˚. 

Example Question #2 : How To Find The Angle For A Percentage Of A Circle

Generalsector

What is the angle measure of \(\displaystyle x\) in the figure above if the sector comprises \(\displaystyle 87%\)% of the circle?

Possible Answers:

\(\displaystyle 298.3\)˚

\(\displaystyle 313.2\)˚

\(\displaystyle 134.9\)˚

\(\displaystyle 101.4\)˚

\(\displaystyle 156.6\)˚

Correct answer:

\(\displaystyle 313.2\)˚

Explanation:

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle.  To do this, you merely need to multiply \(\displaystyle 0.87\) by \(\displaystyle 360\)˚.  This yields \(\displaystyle 313.2\)˚. 

Example Question #3 : How To Find The Angle For A Percentage Of A Circle

What is the angle measure of \(\displaystyle x\) in the figure if the sector comprises \(\displaystyle 37\%\) of the circle?

Generalsector

Possible Answers:

\(\displaystyle 37\)˚

\(\displaystyle 78.4\)˚

\(\displaystyle 133.2\)˚

\(\displaystyle 121.3\)˚

\(\displaystyle 66.6\)˚

Correct answer:

\(\displaystyle 133.2\)˚

Explanation:

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle.  To do this, you merely need to multiply \(\displaystyle 0.37\) by \(\displaystyle 360\)˚.  This yields \(\displaystyle 133.2\)˚

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