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Which polygon has an interior angle sum of 1260°? A polygon has 7 sides. A polygon has 8 sides. A polygon has 9 sides. A polygon has 10 sides.

Respuesta :

Answer:

9 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Equating to 1260 gives

180° (n - 2) = 1260 ( divide both sides by 180 )

n - 2 = 7 ( add 2 to both sides )

n = 9

Thus a polygon with 9 sides

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain. The correct option is C.

What is a polygon?

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The sum of all the interior angles of an 'n' sided polygon is given by the formula,

Sum of all the interior angles = (n-2) × 180°

Given that the sum of the interior angle is 1260°. Therefore, the number of sides n can be calculated as,

1260° = (n-2) × 180°

7 = n - 2

n = 7 + 2

n = 9

Hence, the number of sides the given polygon has is 9.

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