Question

A road sign is in the shape of a regular heptagon. What is the measure of each angle on the sign? Round to the nearest tenth.
900
64.3
231.4

Answer 1

The sum of the interior angles of a polygon is given by\[180°(n -2)\]

Answer 2

Where n is either the total number of interior angles or the total number of edges of a polygon.

Answer 3

A regular polygon is one which has all edges of equal length and all interior angles of equal measure. Thus find the sum of the interior angles of the regular heptagon, and then divide by 7 (because there are 7 interior angles, each of equal measure, in a regular heptagon).

Answer 4

The sum of the exterior angles of a polygon is always 360°. Any exterior angle and its adjacent interior angle are supplementary angles (their sum is 180°). Hence each exterior angle is 360°/n, where n is the total number of edges of the polygon. Consequently, each interior angle is then 180° - 360°/n. Thus alternately, you could also divide 360° by 7, and then subtract the quotient from 180°, to find an interior angle.

Answer 5

Deconstruct the regular heptagon into a bunch of triangles and figure it out from there. That's basically how every geometry problem is solved.