How do you find the sum of the interior angle measures in 24-gon?

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Answer 1 · 2016-12-10T23:12:12

$S = (n - 2)180^@$ For 24 sides: $S = 3960^@$

The general formula for the sum, S, of the measure of the interior angles of a polygon with n sides is:

$S = (n - 2)180^@$

Answer 2 · 2016-12-10T23:20:59

The sum of the interior angles of a $24$ -gon is 3960.

The formula for the sum of the interior angles of a polygon is $(n-2)*180$ , where $n$ is the number of sides.

For a $24$ -gon, $n=24$ .

$(24-2)* 180 = 3960$ .

Another method is to use exterior angles. An $n$ -gon has $n$ exterior angles.

An exterior angles measures $360/n$ .

An interior angle equals $180$ minus the exterior angle.

A $24$ -gon has $24$ exterior angles.

Each exterior angle measures $360/24=15$ .

The interior angle measures $180-15=165$ .

The sum of the $24$ interior angles is then $24*165=3960$ .