Answer:
see explanation
Explanation:
the sum of an exterior angle + interior angle of a polygon = 180°
sum the parts of the ratio 3 : 2 , 3 + 2 = 5 parts
180° ÷ 5 = 36° ← value of 1 part of the ratio , then
3 parts = 3 × 36° = 108° ← interior angle
2 parts = 2 × 36° = 72° ← exterior angle
the sum of the exterior angles of a polygon = 360° , then
= 5 ← number of sides
the sum of the interior angles of a polygon is calculated as
sum = 180° ( n - 2) ← n is the number of sides
if n = 5 , then
sum = 180° × (5 - 2) = 180° × 3 = 540°
and 5 × 108° = 540°
Thus a regular polygon with 5 sides ( Pentagon ) has
interior angle : exterior angle = 3 : 2