Question

Find the measure of an exterior angle of a regular polygon with 19 sides.

Answer 1

Answer: $18.94\°$

Step-by-step explanation:

The exterior angle of a regular polygon of $n$ sides is given by:

$\frac{360\°}{n}$

In the case of a 19-side polygon $n=19$

Hence:

$\frac{360\°}{19}=18.94\°$

Answer 2

Answer:

The measure of the exterior angle is 18. 95 Degrees.

Step-by-step explanation:

Step 1:

Given data:

Let us assume ‘I’ as interior angle of Regular polygon and ‘E’ as Exterior angle of Regular Polygon.

Exterior angle for Regular polygon is 19 sides.

By the formula:

$I=\frac{180(n-2)}{n}$ degrees. ------1.n(s) is the side of polygon.

Step 2:

Substitute the value of n in the given formula. Where n=19 from the given data

$I=\frac{180(n-2)}{n}$degrees

Step 3:

$\begin{array}{l}{I=\frac{180(19-2)}{19} \text { degrees }} \\ {I=\frac{180(17)}{19} \text { degrees }}\end{array}$

I = 3060/19

I = 161.05 degrees.

Step 4:

Measure of the exterior angles of a regular polygon is given by the formula:

E= 360 / n degrees. ----- n(s) side of polygon.

From the given data n are 19.

E = 360 / 19

E= 18. 95 Degrees.