5. Measure of an interior and exterior angle of a regular 16 -gon

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1. A regular 16-gon has $$ n = 16 $$ sides.

2. The measure of each interior angle of a regular $$ n $$-gon is given by  
   $$
   I = \frac{(n - 2) \times 180^\circ}{n}.
   $$
   Substituting $$ n = 16 $$,
   $$
   I = \frac{(16 - 2) \times 180^\circ}{16} = \frac{14 \times 180^\circ}{16}.
   $$
   Simplify the calculation:
   $$
   I = \frac{2520^\circ}{16} = 157.5^\circ.
   $$

3. The measure of each exterior angle of a regular $$ n $$-gon is given by  
   $$
   E = \frac{360^\circ}{n}.
   $$
   For $$ n = 16 $$,
   $$
   E = \frac{360^\circ}{16} = 22.5^\circ.
   $$

4. Therefore, in a regular 16-gon, the interior angle is $$ 157.5^\circ $$ and the exterior angle is $$ 22.5^\circ $$.
In a regular 16-gon, each interior angle is 157.5 degrees and each exterior angle is 22.5 degrees.

Measure of an interior and exterior angle of a regular 16 -gon

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