Question

Determine the measure of an interior angle of the named regular polygon. If a side of the polygon is extended, determine the supplemntsry angle of an interior angle.

A) the measure of each interior angle of a regular hexagon is

B) the measure of the supplementary angle of an interior angle is

Answer 1

A) Each interior angle of the Regular Hexagon = 120°

B)The measure of the supplementary angle of an interior angle is 60°

Explanation:

Regular Hexagon : A 6 sided polygon which has all 6 interior angles as EQUAL is called a regular hexagon.

So, here are 6 interior angles of the hexagon are equal.

Also, Sum of all interior angles of an hexagon = 720°

Let us assume the each angle of the hexagon = m

⇒ m + m + m + m + m + m = 720°

or, 6 m = 720°

or, m = 720° / 6 = 120°

⇒ Each interior angle of the Regular Hexagon = 120°

Now, a side is extended to form an exterior angle.

Let us assume the measure of that exterior angle = k

⇒ k + m = 180 ° ( as k and m are SUPPLEMENTARY ANGLES)

or, k = 180 - 120 = 60 °

or, k = 60 °

Hence, the measure of the supplementary angle of an interior angle is 60°