Question

How many sides does a polygon have if the sum of the measure will of the interior is 10260

Answer 1

The polygon have 59 sides.

Solution:

Sum of the measure of interior angle of the polygon = 10260°

Interior angle theorem of polygon,

The sum of measure of interior angles of a polygon is (n – 2) × 180°.

By this theorem,

(n – 2) × 180° = 10260°

Divide by 180° on both sides.

$\frac{(n - 2) \times 180^\circ}{180^\circ} = \frac{10260^\circ}{180^\circ}$

$n-2=57$

Add 2 on both sides, we get

n – 2 + 2 = 57 + 2

n = 59

Hence the polygon have 59 sides.