What do the angles in a octagon add up to

Asked by maham237 @ 17/02/2021 in Mathematics viewed by 276 People

What is the sum of the EXTERIOR angles of an octagon?

Answered by maham237 @ 17/02/2021

Answer:

A rule of polygons is that the sum of the exterior angles always equals 360 degrees. Since it is a regular octagon, so each of the interior angles of octagon are equal. ((n-2)*180)/n where n is the number of sides of the polygon.for example in case n=8 for an octagon, so we get:

((8-2)*180)/8 => (6*180)/8 => 1080/8 = 135 degrees. This means that each interior angle of the regular octagon is equal to 135 degrees.

Each exterior angle is the supplementary angle to the interior angle at the vertex of the polygon, so in this case each exterior angle is equal to 45 degrees. (180 - 135 = 45). Remember that supplementary angles add up to 180 degrees.

And since there are 8 exterior angles, we multiply 45 degrees * 8 and we get 360 degrees.

This technique works for every polygon, as long as you are asked to take one exterior angle per vertex.

Take any three non-collinear points a b c and draw triangle a,b,c. through each vertex of the triangle draw a line parallel to the opposite side using ruler and compass

Asked by wiki @ 15/11/2022 in Mathematics viewed by 1522 persons

What do the angles in a octagon add up to

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