SOLUTION: a student who was given a pentagon with four angle measures was asked to find the fifth angle the student said he would use [(n-2)times 180]/n. will his method work?

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Question 982289: a student who was given a pentagon with four angle measures was asked to find the fifth angle the student said he would use [(n-2)times 180]/n. will his method work?
Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
That method might or might not work, depending on the pentagon. If not a regular pentagon, it can still be split into separate triangles.

Pick one vertex. Connect this with segments to the two non-adascent vertices. This will form THREE triangles.
180 degrees per triangle
3 triangles
3%2Atriangles%2A%28180%2F1%29%28degrees%2Ftriangle%29=3%2A180=540%2Adegrees

The division by n WILL NOT WORK as a way to find the degrees per angle UNLESS this is a regular polygon. The above calculation is for 540 TOTAL degrees for the interior angles of the pentagon.