Question

Q5. (a) Is it possible to have a regular polygon
with measure of each exterior angle
22°?
(b) Can it be an interior angle of a regular
polygon? Why?
(pls explain if you can)​

Answer 1

(a) Each exterior angle= 22°

∴Number of sides = 360°/22° = 180/11

If it is a regular polygon, then its number of sides must be a whole number.

Here, 180/11 is not a whole number.

∴22° cannot be an exterior angle of a regular polygon

(b) If 22° is an interior angle, then 180° - 22°, i.e., 158° is an exterior angle

∴The Number of sides = 360°/158° = 180°/79 which is not a whole number.

Thus,22°cannot be an interior angle of a regular polygon.