Find the sum of the measures of the interior angles of a convex 30-gon. give answer and show all work.

Question

Find the sum of the measures of the interior angles of a convex 30-gon.         give answer and show all work.

mathstudent55 · Answer

The sum of the measures of the interior angles of an n-sided convex polygon is 

$(n - 2)180$

v-sync · Answer

OK so 

(n - 2)180 =

(30 - 2)180 =
(28)180 = 5040

correct?

mathstudent55 · Answer

Correct.
This formula is easy to remember.

mathstudent55 · Answer

Use 2 less than the number of sides and multiply by 180.
Why 180? It's because 180 is the sum of the measures of the interior angles of a triangle.

mathstudent55 · Answer

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mathstudent55 · Answer

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mathstudent55 · Answer

Notice that for each polygon, the number of triangles you can divide it into is always 2 fewer than the number of sides.
Since each triangle has a sum of measures of angles of 180, multiply 2 fewer than the number of sides to find the sum of the measures of the angles of a polygon.

mathstudent55 · Answer

It is easier to remember the formula if it makes sense to you.

S = (n - 2)180

v-sync · Answer

Thanks