Find the measure of each interior angle and each exterior angle of a regular 18 -gon.

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UpStudy AI · Accepted Answer

1. The measure of each exterior angle for a regular $$ n $$-gon is given by:
   $$
   \text{Exterior Angle} = \frac{360^\circ}{n}
   $$
   For $$ n = 18 $$:
   $$
   \text{Exterior Angle} = \frac{360^\circ}{18} = 20^\circ
   $$

2. The measure of each interior angle is the supplement of the exterior angle:
   $$
   \text{Interior Angle} = 180^\circ - \text{Exterior Angle}
   $$
   Thus:
   $$
   \text{Interior Angle} = 180^\circ - 20^\circ = 160^\circ
   $$

Therefore, each interior angle is $$160^\circ$$ and each exterior angle is $$20^\circ$$.
Each interior angle is 160 degrees, and each exterior angle is 20 degrees.

Find the measure of each interior angle and each exterior angle of a regular 18 -gon.

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