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.
[tex]$\frac{(n - 2) \times 180^\circ}{180^\circ} = \frac{10260^\circ}{180^\circ}[/tex]
[tex]n-2=57[/tex]
Add 2 on both sides, we get
n – 2 + 2 = 57 + 2
n = 59
Hence the polygon have 59 sides.
