(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Solution:
We know that, total sum of all the exterior angles of a regular polygon = 360°
Let the number of sides be = n.
(a) Measure of each exterior angle = 22°
Number of sides = Sum of exterior angles / each exterior angle
= 360°/22°
= 16.36
Thus, we cannot have a regular polygon with an exterior angle of 22° as the number of sides is not a whole number.
(b) Measure of each interior angle = 22°
Measure of each exterior angle = (180 - 22)° = 158°
Number of sides = Sum of exterior angles / each exterior angle
= 360° / 158°
= 2.27
Thus, we cannot have a regular polygon with an interior angle of 22° as the number of sides is not a whole number
Video Solution:
(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°? (b) Can it be an interior angle of a regular polygon? Why?
NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.2 Question 5
Summary:
(a) It is not possible to have a regular polygon with measure of each exterior angle as 22° since the number of sides is not a whole number. (b) It is not possible to have a regular polygon with an interior angle of 22° as the number of sides is not a whole number
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