Question

Fill in the blanks :
In case 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°____

Answer 1

No.of. sides	Each exterior angle	Each interior angle
(i) 8	45°	135°
(ii) 12	30°	150°
(iii) 5	72°	108°
(iv) 8	45°	135°
(v) 12	30°	150°
(vi) 9	40°	140°

Explanation:

(i) Each exterior angle = `360^circ/8 = 45^circ`

Each interior angle = 180° - 45° = 135°

(ii)  Each exterior angle = `360^circ/12 = 30^circ`

Each interior angle = 180° - 30° = 150°

(iii) Since each exterior = 72°

∴ Number of sides = `360^circ/72^circ = 5`

Also interior angle = 180° - 72° = 108°

(iv) Since each exterior = 45°

∴ Number of sides = `360^circ/45^circ = 8`

Also interior angle = 180° - 45° = 135°

(v) Since interior angle = 150°

Exterior angle = 180° - 150° = 30°

∴ Number of sides = `360^circ/30^circ = 12`

(vi) Since interior angle = 140°

Exterior angle = 180° - 140° = 40°

∴ Number of sides = `360^circ/40^circ = 9`