Q5. (a) Is it possible to have a regular polygonwith measure of each e

1.	Q5. (a) Is it possible to have a regular polygonwith measure of each exterior angle22°?(b) Can it be an interior angle of a regularpolygon? Why?(pls explain if you can)
Answer» (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.

Q5. (a) Is it possible to have a regular polygonwith measure of each exterior angle22°?(b) Can it be an interior angle of a regularpolygon? Why?(pls explain if you can)

Answer»

(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.