The polygon have 59 sides.
Solution:
Sum of the measure of interior angle of the polygon = 10260°
Interior angle theorem of polygon,
<em>The sum of measure of interior angles of a polygon is (n – 2) × 180°.</em>
By this theorem,
(n – 2) × 180° = 10260°
Divide by 180° on both sides.
Add 2 on both sides, we get
n – 2 + 2 = 57 + 2
n = 59
Hence the polygon have 59 sides.