How to find the percentage of a sector from an angle

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ISEE Upper Level Quantitative Reasoning › How to find the percentage of a sector from an angle

Questions 1 - 2

Sector SOW has a central angle of $45^{\circ}$ . What percentage of the circle does it cover?

Explanation

Sector SOW has a central angle of $45^{\circ}$ . What percentage of the circle does it cover?

Recall that there is a total of 360 degrees in a circle. SOW occupies 45 of them. To find the percentage, simply do the following:

$\frac{45^{\circ}}{360^{\circ}}*100=.125*100=12.5%$

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of $65^{\circ}$ . What percentage of the circle is highlighted?

Explanation

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of $65^{\circ}$ . What percentage of the circle is highlighted?

To find the percentage of a sector, simply put the degree measure of the angle over 360 and multiply by 100.

$Sector=\frac{65^{\circ}}{360^{\circ}}*100\approx 18.06 %$

So, our answer is 18.06%

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