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3 years ago

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Mathematics

2 answers:

Mars2501 [29]3 years ago

7 0

Answer A interior 140 exterior 40

masha68 [24]3 years ago

3 0

<h3>Answer: Choice A. </h3><h3>interior = 140, exterior = 40</h3>

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Explanation:

For me, I find it easier to find the exterior angle first. For any convex polygon, the sum of the exterior angles is 360 degrees. When we talk about regular polygons with n sides, each exterior angle is 360/n degrees. In this case, we have a nonagon with 9 sides. So n = 9 is plugged into 360/n to get 360/9 = 40 as the exterior angle measure

exterior angle = 40

We could stop here since we can see the answer must be choice A. But let's keep going. To get the interior angle, we subtract the result we got from 180

interior angle = 180-(exterior angle) = 180-40 = 140

This is because any adjacent pair of interior and exterior angles must form a straight angle of 180 degrees.

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side note: you could use the formula $i = \frac{180(n-2)}{n}$ to find the measure of the interior angle.

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