Question

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

Answer 1

Answer:

Sum of the exterior angles of regular polygon =360∘

But each exterior angle =45∘

Number of sides of regular polygon =45∘360∘=8.

Answer 2

Step-by-step explanation:

Q U E S T I O N :

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

S O L U T I O N :

Total measure of all exterior angles = 360°

Measure of each exterior angle = 45°

The number of exterior angles =

$\displaystyle{ \implies \frac{ \cancel{360}}{ \cancel{45}} }$

$\displaystyle{ \implies \: 8}$

∴ The polygon has 8 sides.

MORE INFORMATION :

✪ A simple closed curve made up of only line segments is called a polygon.

✪ There are two types of polygons :

• Convex Polygons
• Convex Polygons

✪ A regular polygon is both "equiangular" and "equilateral".

✪ Sum of all the angles of a triangle is 180°.

✪ To find the sum of all the angles of a polygon the formula is :

• 180° × (n - 2)

Where, n stands for number of sides.

✪ Sum of all the exterior angles of any polygon is 360°.