Question

find the number of sides of a regular polygon whose each exterior angle has a measure of 30 degree.​

Answer 1

Answer:

Total measure of all exterior angle =360°

Measure of each exterior angle = 30°

Therefore,the number of exterior angle=360°/30°

= 12

Hence the polygon has 12 sides.

Answer 2

GIVEN:

each exterior angle = 30°

FIND:

No. of sides of a regular polygon.

SOLUTION:

as we know, that

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

$\bold{ ✪ so, no. \: of \: side \: of \: polygon = \frac{360 \degree}{exterior \: angle} } \\ \bold{\implies \frac{ \cancel{360 \degree}}{ \cancel{30 \degree} }} = 12 \\ \bold{ \longrightarrow no. \: of \: sides = 12}$

$\bold{ Hence, no. \: sides \: of \: a \: regular \: plygon} \\ \bold{whose \: exterior \: angle \: measures \: as \: 30 \degree} \bold{ is \: \boxed{ \bold12.}}$