Examine, if it is possible to have a regular polygon whose each interi

1.	Examine, if it is possible to have a regular polygon whose each interior angle is 110°.
Answer» Here, it is given that the measure of each interior angle of a regular polygon =110° (if possible) Hence, measure of each exterior angle = 180° – 110° = 70°. Suppose number of sides of the polygon = n But sum of all the n exterior angles = 360° ⇒ n x 70° = 360° ⇒ n = \(\frac { 360^o }{ 70^o }\) = 5\(\frac { 1 }{ 7 }\) ≠ a whole number. Hence, a regular polygon having measure of each interior angle 110° can not exist.

Examine, if it is possible to have a regular polygon whose each interior angle is 110°.

Answer»

Here, it is given that the measure of each interior angle of a regular polygon =110° (if possible)

Hence, measure of each exterior angle

= 180° – 110° = 70°.

Suppose number of sides of the polygon = n
But sum of all the n exterior angles

= 360°

⇒ n x 70° = 360°

⇒ n = \(\frac { 360^o }{ 70^o }\)

= 5\(\frac { 1 }{ 7 }\) ≠ a whole number.

Hence, a regular polygon having measure of each interior angle 110° can not exist.