The sun of interior angles of a regular polygon is 1260°.Calculate the number of sides of the polygon and the size of each exterior angle.

a)The number of sides of the polygon = 9 sides

b) The size of each exterior angle = 40°

Step-by-step explanation:

The sun of interior angles of a regular polygon is 1260°.Calculate the number of sides of the polygon and the size of each exterior angle.

a) The number of sides of the polygon

We solve using the formula

S = ( n - 2 ) × 180 °

Where S = Sum of the Interior angles = 1260°

1260° = (n - 2) × 180°

Divide both sides by 180°

1260°/180° = n - 2

7 = n - 2

n = 7 + 2

n = 9 sides

b) The size of each exterior angle

The sum of each exterior angle of a polygon = 360°

Hence, size of each exterior angle = 360°/number of sides of the polygon

= 360°/9

= 40°

300pi

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hard

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