How to Find the Measure of the Central Angle to the Nearest Whole Number Using Percentages of the Circle

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Finding the measure of a central angle will often require you to round to the nearest whole number using percentages. Find the measure of the central angle to the nearest whole number using percentages of the circle in question with help from a longtime mathematics educator in this free video clip.

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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to find the central angle rounding to the nearest whole number using percentages of the circle. Now, it's one of those pretty straight-forward ideas, because, as you know, a circle is 360 degrees. So, to find out the measure of the central angle here and round it to the nearest whole number, what you want to think about is, take the percentage of the circle that you're looking for, and then simply multiply by 360. So, for example, if you know that you want to look for, let's just say, how many degrees 25 percent of the circle is, what you can do is do 25 percent, and then times 360. You can do 0.25 times 360, if you want to convert it that way. Or, you could even do 1/4 of 360 and you'll get 90 degrees here. Or, if you want to think about half, or 50 percent, of the circle, you want to multiply by 360 to find out the measure of the central angle there. Fifty percent is like saying 1/2, times 360, and that'll give you 180 degrees. Now, if it's going to be more technical percentages like 15, 16 percent, then do the same thing. Turn into a decimal, multiply by 360, and then, if it's going to be a decimal answer, then round to the nearest whole number. But, either way, take the percentage, convert it to decimals or fractions, if you want to, and then multiply by 360. So, I'm Jimmy Chang, and that's how to find the measure of the central angle rounding to the nearest whole number using percentages of the circle.

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