How many diagonals are in a decagon?

There is $\binom{10}{2}-10 = 45 - 10 = 35$ .

In a decagon, there are 10 sides and every two points connect a side, we need to eliminate the sides of the decagon that doesn’t form a diagonal.

The diagonals formula is $\frac {n(n-3)}{2}$ for a n-gon. We have to substitute $n=10$ to the formula because a decagon has 10 sides. So $\frac {10 \times 7}{2}$ . Then the answer is $\boxed{35}$ .

Formula: $D=\dfrac{n}{2}(n-3)$

We know that a decagon has 10 sides, now substitute:

$D=\dfrac{n}{2}(n-3)$

$D=\dfrac{10}{2}(10-3)$

$D=5 \times 7$

$D=\boxed{35}$