Answer:
A) Each interior angle of the Regular Hexagon = 120°
B)The measure of the supplementary angle of an interior angle is 60°
Step-by-step 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°
