When a side of a polygon is extended, an exterior angle is formed. In any polygon, the sum of the measures of the exterior angles, one at each vertex, is $$ 360^{\circ} $$. For each regular polygon, find the measure of an exterior angle. $$ \begin{array}{ll} ext { 32. octagon } & ext { 35. } 15 ext {-gon } \ ext { 34. decagon }\end{array} $$

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When a side of a polygon is extended, an exterior angle is formed. In any polygon, the sum of the measures of the exterior angles, one at each vertex, is $$ 360^{\circ} $$. For each regular polygon, find the measure of an exterior angle. $$ \begin{array}{ll}	ext { 32. octagon } & 	ext { 35. } 15 	ext {-gon } \ 	ext { 34. decagon }\end{array} $$

UpStudy AI · Accepted Answer

1. For any regular polygon, the sum of the exterior angles is $$360^\circ$$.

2. To find the measure of each exterior angle, divide $$360^\circ$$ by the number of sides of the polygon.

3. For a regular octagon (8 sides):
   $$
   \text{Exterior Angle} = \frac{360^\circ}{8} = 45^\circ.
   $$

4. For a regular decagon (10 sides):
   $$
   \text{Exterior Angle} = \frac{360^\circ}{10} = 36^\circ.
   $$

5. For a regular 15-gon (15 sides):
   $$
   \text{Exterior Angle} = \frac{360^\circ}{15} = 24^\circ.
   $$

Thus, the measures of the exterior angles are:
- Octagon: $$45^\circ$$
- Decagon: $$36^\circ$$
- 15-gon: $$24^\circ$$
Each exterior angle of a regular polygon is $$360^\circ$$ divided by the number of sides. So: - Octagon (8 sides): $$45^\circ$$ - Decagon (10 sides): $$36^\circ$$ - 15-gon (15 sides): $$24^\circ$$

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