Question

find the measure of a each exterior angle of a regular polygon which has 10 sides

Answer 1

Solution:

Given That:

$\tt \longrightarrow Number\:Of\:Sides(n) = 10$

We know that in any regular polygon, sum of exterior angle is always 360°

Therefore, dividing 360° by the number of sides, we can find the measure of each exterior angle.

Therefore:

$\tt \longrightarrow Measure\:Of\:Each\:Exterior\:Angle = \dfrac{360^{ \circ} }{n}$

$\tt \longrightarrow Measure\:Of\:Each\:Exterior\:Angle = \dfrac{360^{ \circ} }{10}$

$\tt \longrightarrow Measure\:Of\:Each\:Exterior\:Angle = {36}^{ \circ}$

So, the measure of each exterior angle is 36°

Which is our required answer.

Answer:

• The measure of each exterior angle is 36°

Learn More:

In a regular polygon with n number of sides:

$\tt 1. \: Sum\:Of\:Interior\:Angles =(n - 2) \times {180}^{ \circ}$

$\tt 2. \: Sum\:Of\:Exterior\:Angles ={360}^{ \circ}$

If any of the exterior angle is known:

$\tt 3. \: Number\:Of\:Sides = \dfrac{360}{Exterior\:Angle}$

If the answer for above is not a natural number, no such polygon exists.