Question

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 1

Answer :

The  number of sides of the polygon is 8

Step-by-step explanation :

Given that :

The sum of the interior angles of a polygon is 3 times the sum of its exterior angles.

To Detemine :

The  number of sides of the polygon.​

Solution :

We know :

Sum of the exterior angles of a regular polygon is 3 times the sum of its exterior angles = 360°

Hence,

Sum of interior angles = 3 × 360° = 1080°

Now,

We have sum of interior angles s = (x - 2) 180°

Note :

"x" is the number of sides of the polygon.

Put the values :

$\tt \implies (x-2)180^{\circ}=1080^{\circ }\\ \\\implies x-2=6\\ \\\implies x=8$

$\bigstar \textbf{\underline{\underline{Hence, The number of sides of the polygon is 8(x=8)}}}$

Answer 2

Answer :-

The number of sides of the polygon is 8.

Step-by-step explanation:

Sum of the exterior angles of a regular polygon is 3 times the sum of its exterior angles = 360°

.°. Sum of interior angles = 3 × 360° = 1080° .........(I)

Again, we have

Sum of interior angles as

s = (n - 2)180° .........(II)

where, "n" is the number of sides of polygon

from equation (I) & (II), we get

(n - 2)180° = 1080°

=> n - 2 = 1080/180

=> n - 2 = 6

=> n = 8

Hence, the polygon of 8 sides is octagon.