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Given the regular polygon, find the measure of each numbered angle.

 

 Apr 16, 2020
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we know the whole way around the center is 360 degrees and since it's divided into 8 sections (not including the line that goes straight down) we can divide 360/8 to get 45 degrees for angle 1. Angle 2 is in the same triangle but just split in half, so since we already figured out what angle 1 is, we just split it in half to get angle 2. 45/2 = 22.5 degrees. Lastly, all triangles have to have their angles add up to 180 degrees so for number 3, we just figure out the other two angles in the small triangle that it's in. We know angle 2 is 22.5 and that the other angle is 90 degrees because the little square at the bottom of the octagon. That means for the little triangle that angle 3 is in, the angles are 22.5 degrees (angle 2), 90 degrees (given by the picture), and angle 3 (which we're trying to find) and it all adds up to 180 degrees. So the final step is taking the 180 degrees and subtracting 22.5 and 90 to get that angle 3 is 67.5 degrees.

 Apr 16, 2020

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