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

Question

asked Nov 27, 2024 13.9k views

2 Answers

Mike Tsayper · Answer 1 · 2024-11-30T03:36:29+0000

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