I chose D because I thought this only applies to regular polygons and it doesn’t mention that it is regular.
Am I wrong?
Instead of memorizing facts, you should try to reason out why that might be the case. In this case, it isn’t.
You can imagine partitioning any concave n-polygon (those with reflex angles) into n triangles. You then subtract off the central angles which then leads you to:
180^{\circ}(n) - 360^{\circ} = 180^{\circ}(n) - 180^{\circ}(2) = (n-2) 180^{\circ}
In other words, this the sum of interior angles holds for both convex and concave polygons alike. It has little to do with regular or irregular polygons tbh.
Hmm…I’m having a hard time understanding what you are saying.
I’m not too sure how convex and concave polygons are related to this question.
Because this seems like the more interesting question to answer (and maybe what you intended indirectly). Idk what regular and irregular polygon would achieve for you. This would be like saying the sum of the internal angles of a triangle, which isn’t an equilateral triangle (regular), is different.
Anyway, the main idea behind what i’m saying is that your formula for the regular case also holds for the irregular case.
As in, your hunch was wrong and the polygon doesn’t have to be regular.
@Leaderboard @ganesh I’m curious to hear your response to this.
I thought whether the polygon is regular or not is important. If the polygon isn’t regular, doesn’t that mean that each interior angle could be all different?
Or for this question because it’s asking about the sides, does the regular thing not matter?
IF this question asked what each interior angle equals to, would I be able to solve this without knowing whether this polygon is regular or not?
Basically what cylverixxx said.
Yes, but the sum still remains the same even if the angles themselves could be different. If the question asked for the measure of each interior angle, then yes you are right.
Then it’s a D.
One note @cylverixxx concave polygons do not show up on the GRE as per the GRE Math Conventions.
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