Question : If the sum of the measures of all the interior angles of a polygon is 1440$^\circ$, find the number of sides of the polygon.
Option 1: 8
Option 2: 12
Option 3: 10
Option 4: 14
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Correct Answer: 10
Solution :
Given: If the sum of the measures of all the interior angles of a polygon is 1440$^\circ$.
A polygon with $n$ sides has an interior angle sum of $(n – 2)×180^\circ$.
According to the question,
$(n – 2)×180^\circ=1440^\circ$
⇒ $n–2=8$
⇒ $n=10$
Hence, the correct answer is 10.
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