[Math] How many “ANGLES” does a pentagon have

geometry

If asked "How many angles does a pentagon have?" would the exterior and interior angles count as 2 angles for each vertex?

Best Answer

Well, one can argue and justify a variety of answer but it comes down to what we mean when we ask the question.

I figure if we ask how many angles a pentagon has we absolutely should mean exactly the same thing as when we ask how many angles does any type of polygon have.

And if we ask how many angles a triangle has the universally accepted answer is ... $3$.

So what do we mean by that?

Presumably we mean how many interior angles and we assume one interior angle at each vertex.

So if we mean the same thing then the answer to "how many angles does a pentagon have" should be $5$.

Of course, we could (and many of us will; we just can't help ourselves... we are mathematicians after all) argue that a triangle really has $6$ angles because we should count exterior angles. But such arguments are usually met with a smirk and walking away.

The answer is $5$.

Related Question