Look how he has proved that
2 answers:
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<h3>Answer: 1440 degrees</h3>
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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.