Question

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

Answer 1

Answer:

40°

Step-by-step 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:

$\alpha=\dfrac{180^o(n-2)}{n}$

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

$\alpha=\dfrac{180^o(9-2)}{9}=(20^o)(7)=140^o$

$180^o-140^o=40^o$

Method 2:

Look at the picture.

$\alpha=\dfrac{360^o}{9}=40^o$

$2\beta$ - 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:

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

Answer 2

Answer:

40°

Step-by-step 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°.