Using exterior angle property of polygons to find the number of sides:
It is known that the measure of each interior angle is 165°.
Then, each exterior angle = 180°-165° [∵exterior angle = 180°- interior angle]
⇒ 15°
∵ (number of sides) × (the measure of each exterior angle) =360° [Using exterior angle property of polygons]
⇒ (number of sides) ×15° = 360°
⇒ Number of sides = 360°/15°
⇒ 24
Therefore, a polygon with interior angles 165° has 24 sides.
