Question

What is the measure of an exterior angle of a regular 7-sided polygon?

Enter your answer as a decimal in the box.

Round to the nearest tenth of a degree.

Answer 1

The sum of internal angles in an n-sided polygon is 180(n-2).

In a regular 7-sided polygon, the sum of the internal angles is
180*(7 - 2) = 900°
Each internal angle is  900/7 = 128.57°.

Because the sum of angles on one side of a straight line is 180°. therefore
each exterior angle is 180 - 128.57 = 51.43°

Answer: 51.4°  (nearest tenth)

Answer 2

Answer: $51.4^{\circ}$

Step-by-step explanation:

We know that the sum of all the exterior angles of a regular polygon with n sides is $360^{\circ}$.

The measure of an exterior angle of a regular n-sided polygon is given by :-

$\dfrac{360^{\circ}}{n}$

Now, the measure of an exterior angle of a regular 7-sided polygon is given  by :-

$\dfrac{360^{\circ}}{7}=51.4285714286^{\circ}\approx51.4^{\circ}$

Hence, the  measure of an exterior angle of a regular 7-sided polygon =$51.4^{\circ}$