20 second problem

Geometry Level 2

Find the inside angle ( in degrees ) of a regular octagon.

Note that an octagon has 8 8 sides .

The answer is 135.

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3 solutions

The sum of the exterior angles of a convex polygon is 360 degrees. The interior and exterior angles are complements (i. e., add to 180 degrees). Therefore the answer, in this case, is 180 360 8 135 180-\frac{360}{8}\Rightarrow 135 .

Hana Wehbi
May 5, 2019

There is a short cut formula for the interior angle of a regular polygon which is:

( n 2 ) × 18 0 n \frac{(n-2)\times 180^\circ}{n} where n n is the number of sides of the regular polygon. Thus, the measure of the interior angle is: 6 × 18 0 8 = 13 5 \frac{6\times180^\circ}{8}=135^\circ

Magnus Käärik
May 4, 2019

The formula for finding the sum of all the angles that are inside is (n-2)×180. In this case n=8. so the sum of all the inside angles is 6×180=1080. Since there are 8 inside angles in total one inside angle is equal to 1080:8=135 degrees.

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