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?
1 answer:
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°
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