Question

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

Answer 1

Hey there! We need to use this following formula for finding the sum of interior angles:

$sum=180\left(n-2\right)$

We know that the sum of exterior angles is always 360°. The question also stated that sum of interior angles is 6 times the sum of exterior angles. We can write an equation for this!

$sum=6 \times 360$

$sum=2160$

We can now also use the original formula at the LHS, as follows:

$sum=2160$

$180\left(n-2\right)=2160$

We can cancel the 180 and the 2160, so we will get this:

$n-2=12$

$n=14$

Therefore, the polygon has 14 sides.

Answer 2

Answer: 14 sides

Step-by-step explanation: 180(n-2)

sum= 6×360

sum= 2160

180(n-2)=2160