Question

Find the number of sides of a regular polygon whose each exterior angle has a measure of 45degree​

Answer 1

Answer:

each exterior angle =45

each interior angle = 180-45 =135

let angle subtended at center be a

as it is regular polygon so joining side to center

becomes isosceles triangle

Sum of angles to equal .side = 135

So central angle =180-135=45

As central angle = 2Π/n =45

n = 360/45

n = 8

so no of sides are 8

Answer 2

Answer:

$Sum of exterior angle of any polygon is 360o . As each exterior angle is 45o ,number of angles or sides of thepolygon is 360o45o=8 . Further aseach exterior angle is 45o , eachinterior angle is 180o−45o=135o .$