Question

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

Answer 1

interior angle would be 135

as interior angles is (n-2) 360/n = 135

360n - 720 -135 n =0

Answer 2

GIVEN:

each exterior angle = 45°

FIND:

No. of sides of a regular polygon.

SOLUTION:

as we know, that

☞ In a regular polygon sum of all interior angle is 360°.

$\bold{ ✪ so, no. \: of \: side \: of \: polygon = \frac{360 \degree}{exterior \: angle} } \\ \bold{\implies \frac{ \cancel{360 \degree}}{ \cancel{45 \degree} }} = 8\\ \bold{ \longrightarrow no. \: of \: sides = 8}$

$\bold{ Hence, no. \: sides \: of \: a \: regular \: plygon} \\ \bold{whose \: exterior \: angle \: measures \: as \: 45 \degree} \bold{ is \: \boxed{ \bold8.}}$