Question

Find the measure of one exterior angle of the following polygon:
Nonagon

Answer 1

40°

Explanation:

1. Shape of a nonagon: 9 (root non-)

2. Total exterior angle: 360° (constant for all polygons)

3. Given that this polygon is regular, the one exterior angle of an nonagon is 360°/9 = 40°.

Answer 2

40°

Explanation:

An exterior angle and an interior angle are supplementary angles.

Two Angles are Supplementary when they add up to 180°.

Therefore the measure of exterior angle is equal to different between 180° and an interior angle.

Method 1:

You can use the formula of the measure of interior angle of the regular polygon with n-sides:

`\alpha=(180^o(n-2))/(n)`

We have a nonagon. Therefore n = 9. Substitute:

`\alpha=(180^o(9-2))/(9)=(20^o)(7)=140^o`

`180^o-140^o=40^o`

Method 2:

Look at the picture.

`\alpha=(360^o)/(9)=40^o`

`2\beta` - it's an interior angle

We know: The sum of measures of these three angles of any triangle is equal to 180°.

Therefore:

`\alpha+2\beta=180^o\to2\beta=180^o-\alpha`

Substitute:

`2\beta=180^o-40^o=140^o`

`\theta` - it's a exterior angle

`2\beta+\theta=180^o\to\theta=180^o-2\beta`

substitute:

`\theta=180^o-140^o=40^o`