How to find the angle for a percentage of a circle

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

Questions 1 - 2

Sector TYP occupies 43% of a circle. Find the degree measure of angle TYP.

$154.8^{\circ}$

$15.5^{\circ}$

$430^{\circ}$

$366^{\circ}$

Sector TYP occupies 43% of a circle. Find the degree measure of angle TYP.

Use the following formula and solve for x:

$\frac{x}{360^{\circ}}100=43%$

Begin by dividing over the 100

$\frac{x}{360^{\circ}}=.43$

Then multiply by 360

$x=.43*360^{\circ}=154.8^{\circ}$

If sector AJL covers 45% of circle J, what is the measure of sector AJL's central angle?

$162^{\circ}$

$45^{\circ}$

$145^{\circ}$

$262^{\circ}$

If sector AJL covers 45% of circle J, what is the measure of sector AJL's central angle?

To find an angle measure from a percentage, simply convert the percentage to a decimal and then multiply it by 360 degrees.

$45%\rightarrow 0.45$

$0.45 * 360^{\circ}=162^{\circ}$

So, our answer is 162 degrees.