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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