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

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°.

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:

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

Method 2:

Look at the picture.

- it's an interior angle

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

Therefore:

Substitute:

- it's a exterior angle

substitute:

c. side angle side. u shares the same sides