Question : The interior angle of a regular polygon exceeds its exterior angle by 90°. The number of sides of the polygon is:
Option 1: 8
Option 2: 6
Option 3: 10
Option 4: 12
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Correct Answer: 8
Solution :
Given: The interior angle of a regular polygon exceeds its exterior angle by 90°.
Let $x$ be the polygon's exterior angle and $n$ be its number of sides.
A regular polygon's sum of its exterior and interior angles = 180°.
A regular polygon's exterior angle = $\frac{360°}{n}$, where $n$ is the number of sides.
According to the question,
$x+x+90°=180°$
⇒ $2x=90°$
⇒ $x=45°$
The number of sides of the polygon is given as,
$45°=\frac{360°}{n}$
⇒ $n=8$
Hence, the correct answer is 8.
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