Answer :
Final answer:
The sum of interior and exterior angles in a polygon can be found using specific formulas, leading to the identification of the decagon as the polygon in this case.
Explanation:
The sum of interior and exterior angles of a polygon: In a polygon, the sum of the measures of interior angles is given by 180(n-2) where n is the number of sides. The sum of the exterior angles of any polygon is always 360 degrees.
Finding the polygon: To find the polygon where the sum of interior and exterior angles is 1440°, we use the formula 180(n-2) + 360 = 1440. Solving this equation gives n=10, indicating it is a decagon (10-sided polygon).
Example: In a decagon, the sum of interior angles = 180(10-2) = 1440° and the sum of exterior angles = 360°.
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