Angles and Degrees for Dummies

Irregular polygon angles

One of the staffers was trying to get the office Google Home to play a radio station not long ago and found that the station's relationship with TuneIn was... fraught. She had to specify not just the call letters, but also the frequency and streaming service to get her tunes; e.g., "Play KLMN 100.7 on TuneIn." If she expanded the request to, "Play KLMN 100.7 FM on TuneIn," Ms Google would say, "I think you want to listen to the radio. Is that right?" Google's or TuneIn's screwup notwithstanding, there's a lesson there. It's a lesson eHowian Karl Wallilus should have learned before pounding out the Sciencing.com post "How to Find Degrees in Polygons."

Leaf Group did not serve Wallulis well when they ported his original over from its original at eHow.com, blowing the transcription of what Wallulis originally wrote – 

"The sum of all the degrees of the interior angles equals (n - 2)*180"

 – to create the nonsensical 

"The sum of all the degrees of the interior angles equals(n - 2)_180 [sic]."

That's not on Karl, although SOMEONE should have fixed it in the past several years. What IS on Wallulis, however, is his failure to disabuse the OQ of the notion that "Find degrees in polygons" has any particular meaning. But, then, Karl had some other problems as well. Take, for instance, his notion that,

"Polygons are typically classified according to number of sides and the relative measures of its sides and angles."

Besides being non-parallel (ba-dump-bump), this geometric statement is incorrect. Polygons are classified by the number of sides, whether or not they are regular, and – if irregular – whether they are concave, convex, or even degenerate. He also seems confused about the language of mathematics (in this case, geometry). For instance, his first step in "finding the degrees" is to,

"Add the number of sides of the polygon."

Ummm, Karl, "add the number" to what? Oh, we get it, you mean count the number of sides. And then there are these... interesting constructions:

"This is the degree of each angle in the polygon... [and] This is the degree of every exterior angle on the polygon."

Besides the unfortunate fact that Karl seems to think all polygons are regular (obviously, they aren't), he failed to educate his readers and the OQ by explaining that this is the value of the exterior angle, not the "degrees." Whaddaninjit.

We find it instructive that Walluls said, twice, "If the polygon is regular..." His ignorance led him to explain to his readers that,

"Calculate the supplement of the angle from Step 2 (180 minus the degree) to find the exterior angle measure of a regular polygon."

What our Dumbass of the Day should have said here is that, regardless of whether a polygon is regular or irregular, the exterior angle is the supplement of the interior angle; its supplementary angle (not, as Karl said, its "supplemental angle"). Feh.

MM - GEOMETRY