Question

The exterior angle of a pentagon are in the ratio 1:2:3:4:5.find all the interior angles of a pentagon

Answer 1

Exterior angles sum are always 360° in any polygon so
let the ext. angle be x, 2x, 3x, 4x and 5x respectively so now
$x + 2x + 3x + 4x + 5x = 360 \\ 15x = 360 \\ x = 360 \div 15 \\ x = 24 \\ 2x = 24 \times 2 = 48 \\ 3x = 24 \times 3 = 72 \\ 4x = 24 \times 4 = 96 \\ 5x = 24 \times 5 = 120$
now int. angle + ext. angle = 180° (linear pair)
so
angle 1 = 180 - 24= 156
angle 2= 180 - 48= 132
angle 3= 180 - 72 = 108
angle 4= 180 - 96= 84
angle 5= 180 - 120 =60
hope it helps