Question

Find the interior angle sum of this polygon. Can someone help????

Answer 1

Answer:  1440 degrees

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Explanation:

See the diagram below. It shows there are 10 sides, so n = 10.

We'll plug this value of n into the formula below to find the sum of all ten interior angles

S = sum of interior angles

S = 180(n-2)

S = 180(10-2)

S = 180(8)

S = 1440 degrees

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A different approach:

Let's assume this polygon is a regular polygon. This means each angle is congruent to one another.

We have n = 10 sides, so each exterior angle is E = 360/n = 360/10 = 36 degrees.

Each interior angle adjacent to this 36 degree exterior angle is

180-E = 180-36 = 144 degrees

Since we have 10 equal angles of 144 degrees each, so overall the interior angles add to 10*144 = 1440 degrees

Side note: if this polygon is not a regular polygon, then this section does not apply. You would use the first method instead.