Question

Fill in the blanks:

In case of regular polygon, with

Number of sides	Each exterior angle	Each interior angle
(i) 6	_________	__________
(ii) 8	_________	__________
(iii)  ________	36°	__________
(iv)  _______	20°	__________
(v)  _________	_________	135°
(vi) ________	_________	165°

Answer 1

Number of sides	Each exterior angle	Each interior angle
(i) 6	60°	120°
(ii) 8	45°	135°
(iii)  10	36°	144°
(iv)  18	20°	160°
(v)  8	45°	135°
(vi) 24	15°	165°

(i) Each exterior angle = `360^circ/6 = 60^circ`

Each interior angle = 180° - 60° = 120°

(ii) Each exterior angle = `(360°)/8` = 45°

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

(iii) Since each exterior angles = 36°

∴ Number of sides = `(360°)/(36°) = 10`

Also, interior angle = 180°- 20° = 160°

(iv) Since each exterior angles = 20°

∴ Number of sides = `(360°)/(20°) = 18`

Also, interior angle = 180° - 20° = 160°

(v) Since interior angles = 135°

∴ exterior angle = 180° - 135° 

∴  Number of sides = `(360°)/(45°) = 8`

(vi) Since interior angle = 165°

∴ exterior angle = 180° - 165° = 15°

∴ Number of sides = `(360°)/(15°) = 24`