Question

In which polygon is the sum of the number of sides and the number of diagonals equal to 105?​

Answer 1

Answer: 15-agon

Explanation:

Sum of number of sides , n

formula for number of diagonals =

`(n(n-3))/(2)`

If you added the 2 and made = 105

n +
`(n(n-3))/(2)` = 105

multiply everything by 2 to get rid of fraction

2n + n(n-3) =210

2n + n² - 3n = 210

n²-n -210 =0 factor

(n-15)(n+14)=0 set each =0 and solve can't get - so -14 is invalid

n=15

Answer 2

Decagon

Explanation: