Missing Angles for Dummies

Internal angles, irregular polygon

For a time, a few years back, a certain demographic seemed to be obsessed with angels. For the record, by the way, no one here at the Antisocial Network was in that group... or admits to it, that is. Anyway, when we ran across the title of today's DotD nominee, we get the distinct impression that freelancer and fashion blogger Aksana Nikolai thought that someone was looking for a winged celestial being when she (probably not he) asked "How to Find a Missing Angle." Imagine her surprise when she googled the phrase and learned it has something to do with geometry...

Nikolai began, as eHowians were so required, with an introduction:

"A triangle is a three-sided polygon. Instructors often ask intermediate and advanced-level math students to calculate the missing angle in a triangle."

At this point, we carefully examined the original question. We even asked an intern to proofread it. Nowhere, however, does the word "triangle" appear in the original question. In other words, Aksana decided – for some reason (probably innumeracy) – that only triangles can have missing angles. To that end, she pounded out two different methods of determining the "missing angle":

"One method of finding a missing angle is based on the premise that the sum of the interior angles of a triangle equals 180 degrees. Another approach involves using a formula based on the trigonometric sine rule."

Most fifth-graders can address the first case (angle C = 180 - (Angle A + Angle B)), and Nikolai therefore had no problem. Her second approach required that she know a little about geometry, which we suspect she found a tad on the puzzling side as one might determine from this statement:

"If you are unsure whether the angle is obtuse or acute, measure it with a protractor..."

...after which she botched the explanation of sine and the law of sines. But we're not here to argue about her examples; we're here to point out that you can have a missing angle in any polygon and that Nikolai completely blew it when she pretended that only triangles need apply!

We'd like to think that a freelancer with some sort of STEM background (as opposed to "international affairs") might have mentioned, even if only in one of eHow's TIPS, that the sum of the internal angles in a polygon with n sides is 180 * (n-2). Consequently, you can determine the missing angle of any irregular polygon from the sum of the known angles... something Aksana should have known, and mentioned, but didn't – hence the Dumbass of the Day award.

copyright © 2018-2022 scmrak

MM - GEOMETRY