Question

Find The Number of sides of a polygon if the sum of its interior angles are
1440°​

Answer 1

Answer:

The sum of the measures of the interior angles of a decagon (10 sided polygon) is 1,440. We found this by using the formula (n-2)(180). Thus, to find the measure of each interior angle we simply divide the sum by the number of total sides in the polygon. 1,440/10 = 144..

Step-by-step explanation:

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Answer 2

$Sum \: of \: Interior \: angle \: \: of \\ Polygon = 1440°$

$(2n - 4) \times 90° = 1440°$

$2n - 4 = \frac{1440°}{90°}$

$2(n - 2) = \frac{1440°}{90°}$

$n - 2 = \frac{1440°}{2 \times 90°}$

$n - 2 = 8$

$n = 8 + 2$

$n = 10$