Question

Given a regular hexagon, what are the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon?

Answer 1

Answer:

a)  60°

b)  60°

Step-by-step explanation:

A regular hexagon can be broken down into 6 equilateral triangles.

*** Note: Attached picture shown.

a)

The angle between two consecutive radii would be taken as EO and OD.

Since all of these 6 angles (of 6 triangles) create a circle, the sum is 360. So each angle (between two radii) would be 360/6 = 60°

b)

To find angle between side and radius of a polygon, let's take the radii as EO and side as ED.

Since we already found the angle between 2 radii to be 60, we have two angle left of a triangle (same size, let's call it x). We know sum of 3 angles in a triangle is 180, thus we can write:

60 + x + x = 180

60 + 2x = 180

2x = 180 - 60

2x = 120

x = 120/2

x = 60°