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:
[tex]\alpha=\dfrac{180^o(n-2)}{n}[/tex]
We have a nonagon. Therefore n = 9. Substitute:
[tex]\alpha=\dfrac{180^o(9-2)}{9}=(20^o)(7)=140^o[/tex]
[tex]180^o-140^o=40^o[/tex]
Method 2:
Look at the picture.
[tex]\alpha=\dfrac{360^o}{9}=40^o[/tex]
[tex]2\beta[/tex] - it's an interior angle
We know: The sum of measures of these three angles of any triangle is equal to 180°.
Therefore:
[tex]\alpha+2\beta=180^o\to2\beta=180^o-\alpha[/tex]
Substitute:
[tex]2\beta=180^o-40^o=140^o[/tex]
[tex]\theta[/tex] - it's a exterior angle
[tex]2\beta+\theta=180^o\to\theta=180^o-2\beta[/tex]
substitute:
[tex]\theta=180^o-140^o=40^o[/tex]
