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attashe74 [19]
3 years ago
11

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

Mathematics
2 answers:
Contact [7]3 years ago
5 0

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\°

Elza [17]3 years ago
4 0

Answer:

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

Step-by-step explanation:

<u>Step 1: </u>

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.

<u>Step 2: </u>

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

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

<u>Step 3: </u>

\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.

<u>Step 4: </u>

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.

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