Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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Exterior Angles of a Polygon - Problem 2

Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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An exterior angle is the angle constructed by extending a side of a polygon. The sum of the exterior angles of a polygon is 360°, regardless of the number of sides, if it is regular, or equiangular. So, given the other exterior angles, it is possible to find a missing exterior angle of a polygon. Simply add up the given exterior angles and subtract it from 360°.

We can use what we know about exterior angles that is, that exterior angles will always sum to 360 degrees no matter how many sides you have. To solve for missing angles: so in this problem right here we have a pentagon, but it doesn’t really matter because we know that the sum of the 5 exterior angles will always be 360 degrees.

So looks like we’re missing a measure right here, but since this is a linear pair, I know that has to be 90 degrees and I know that this is a linear pair, so if the interior angle is 80 the exterior angle will be 100 degrees. And last, since we have another linear pair, this extra angle must be 60 degrees. So I’m going to write an equation that says 360 is equal to the sum of the exterior angles which we know everyone except for x. So I’m gong to say 90 plus 80 plus 60 plus 100 plus x. So the sum of those; 1, 2, 3, 4, 5 exterior angles must be 360 degrees.

So now it’s time to test Mr. McCall’s mental Math. So 90 and 80 is 170, plus 60 is 230, plus 100 is 330, plus x, a lot of confidence in that number. So last step is we’re going to subtract the 330 from both sides of this equation and x is 30 degrees.

Again the key thing here is remembering that the sum of your exterior angles will always, always, always be 360 degrees.

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