The sum of the interior angles of a polygon is three times the sum of

1.	The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon.
Answer» By using the formulas, The sum of interior angles of a polygon = (n – 2) × 180° …..(i) The Sum of exterior angle of a polygon is 360° So, Sum of interior angles = 3 × sum of exterior angles = 3 × 360° = 1080°…..(ii) Now by equating (i) and (ii) we get, (n – 2) × 180° = 1080° n – 2 = 1080^o/180^o n – 2 = 6 n = 6 + 2 = 8 ∴ Number of sides of a polygon is 8.

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon.

Answer»

By using the formulas,

The sum of interior angles of a polygon = (n – 2) × 180° …..(i)

The Sum of exterior angle of a polygon is 360°

So,

Sum of interior angles = 3 × sum of exterior angles

= 3 × 360° = 1080°…..(ii)

Now by equating (i) and (ii) we get,

(n – 2) × 180° = 1080°

n – 2 = 1080^o/180^o

n – 2 = 6

n = 6 + 2

= 8

∴ Number of sides of a polygon is 8.