Question

If the total sum of the interior angles is `900°` , how many sides does the polygon have ?

Answer 1

Please see below.

Explanation:

Sum of exterior angles of any polygon is always `360^@`, it can never be `900^@`. Hence, there cannot be any polygon like this.

It appears that by error the word "exterior" has been mentioned. In case sum of interior angles is `900^@`,

total sum of all the angles is `900^@+360^@=1260^@`.

But sum of each pair of interior and exterior angles add up to `180^@`

we have `(1260^@)/(180^@)=7` such pairs

and hence polygon has `7` sides.

Answer 2

`7` sides

Explanation:

You can use the formula for finding the sum of the interior angles:

`S = 180(n-2)" "` where `n` is the number of sides

If the sum is `900°` we have:

`180(n-2)=900`

`n-2 = 900/180`

`n-2 =5`

`n = 5+2=7`

There are `7` sides.