Fill in the blanks:

Incase of regular polygon, with:

no. of sides	each exterior angle	each interior angle
(i) ..8…………	……………	……………
(ii)..12…..	……………	……………
(iii) ……………	..72°……….	……………
(iv) ……………	..45°……….	……………
(v) ……………	……………	….150°…….
(vi) ……………	……………	….140°…….

(i) As per the properties of polygon, if there are n number of sides then each of its exterior angles is $\dfrac{360°}{n}$.

n = 8

⇒ $\dfrac{360°}{8}$ = 45°

Hence, each exterior angle = 45°.

As per the properties of polygon, if there are n number of sides then each of its interior angles is $\dfrac{(2n - 4)90°}{n}$.

= $\dfrac{(2 \times 8 - 4) \times 90°}{8}$

= $\dfrac{(16 - 4) \times 90°}{8}$

= $\dfrac{12 \times 90°}{8}$

= $\dfrac{1080°}{8}$

= 135°

Hence, each interior angle = 135°.

(ii) As per the properties of polygon, if there are n number of sides then each of its exterior angles is $\dfrac{360°}{n}$.

n = 12

⇒ $\dfrac{360°}{12}$ = 30°

Hence, each exterior angle = 30°.

As per the properties of polygon, if there are n number of sides then each of its interior angles is $\dfrac{(2n - 4) 90°}{n}$.

= $\dfrac{(2 \times 12 - 4) \times 90°}{12}$

= $\dfrac{(24 - 4) \times 90°}{12}$

= $\dfrac{20 \times 90°}{12}$

= $\dfrac{1800°}{12}$

= 150°

Hence, each interior angle = 150°.

(iii) As per the properties of polygon, if there are n number of sides then each of its exterior angles is $\dfrac{360°}{n}$.

Exterior angle = 72°

⇒ $\dfrac{360°}{n}$ = 72°

⇒ n = $\dfrac{360°}{72°}$

⇒ n = 5

Hence, number of sides = 5.

As per the properties of polygon, if there are n number of sides then each of its interior angles is $\dfrac{(2n - 4) \times 90°}{n}$.

n = 5

= $\dfrac{(2 \times 5 - 4) \times 90°}{5}$

= $\dfrac{(10 - 4) \times 90°}{5}$

= $\dfrac{6 \times 90°}{5}$

= $\dfrac{540°}{5}$

= 108°

Hence, each interior angle = 108°.

(iv) As per the properties of polygon, if there are n number of sides then each of its exterior angles is $\dfrac{360°}{n}$.

Exterior angle = 45°

⇒ $\dfrac{360°}{n}$ = 45°

⇒ n = $\dfrac{360°}{45°}$

⇒ n = 8

Hence, number of sides = 8.

As per the properties of polygon, if there are n number of sides then each of its interior angles is $\dfrac{(2n - 4) \times 90°}{n}$.

n = 8

= $\dfrac{(2 \times 8 - 4) \times 90°}{8}$

= $\dfrac{(16 - 4) \times 90°}{8}$

= $\dfrac{12 \times 90°}{8}$

= $\dfrac{1080°}{8}$

= 135°

Hence, each interior angle = 135°.

(v) As per the properties of polygon, if there are n number of sides then each of its interior angles is $\dfrac{(2n - 4) \times 90°}{n}$.

⇒ $\dfrac{(2n - 4) \times 90°}{n}$ = 150°

⇒ (2n - 4) x 90° = 150°n

⇒ 180°n - 360° = 150°n

⇒ 180°n - 150°n = 360°

⇒ 30°n = 360°

⇒ n = $\dfrac{360°}{30°}$

⇒ n = 12

Hence, number of sides = 12.

As per the properties of polygon, if there are n number of sides then each of its exterior angles is $\dfrac{360°}{n}$

⇒ $\dfrac{360°}{12}$ = 30°

Hence, each exterior angle = 30°.

(vi) As per the properties of polygon, if there are n number of sides then each of its interior angles is $\dfrac{(2n - 4) \times 90°}{n}$.

⇒ $\dfrac{(2n - 4) \times 90°}{n}$ = 140°

⇒ (2n - 4) x 90° = 140°n

⇒ 180°n - 360° = 140°n

⇒ 180°n - 140°n = 360°

⇒ 40°n = 360°

⇒ n = $\dfrac{360°}{40°}$

⇒ n = 9

Hence, number of sides = 9.

As per the properties of polygon, if there are n number of sides then each of its exterior angles is $\dfrac{360°}{n}$.

⇒ $\dfrac{360°}{9}$ = 40°

Hence, each exterior angle = 40°.