Question : If a regular polygon has 16 sides, then what is the measure (in degrees) of each interior angle?
Option 1: $154$
Option 2: $157 \frac{1}{2}$
Option 3: $155$
Option 4: $159 \frac{1}{2}$
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Correct Answer: $157 \frac{1}{2}$
Solution :
Here, the number of sides, $n=16$
According to the question,
Each exterior angle $=\frac{360}{n}=\frac{360}{16}=\frac{45}{2}$
Now,
⇒ Interior angle + Exterior angle = 180
⇒ Interior angle = $180 - \frac{45}{2}=\frac{315}{2}= 157\frac{1}{2}$
Hence, the correct answer is $157\frac{1}{2}$.
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