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

2 Answers
Dec 10, 2016

Answer:

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

Explanation:

Here is a reference Interior angles of a polygon

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^@#

Dec 10, 2016

Answer:

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

Explanation:

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#.