A square has two diagonals, and a convex pentagon has five diagonals.  How many diagonals does a convex decagon have?
A convex $n$-gon has $\frac{n(n-3)}{2}$ diagonals. Thus, a convex decagon has $\frac{10\cdot 7}{2} = \boxed{35}$ diagonals.
35
Level 5
Prealgebra
Problem: A square has two diagonals, and a convex pentagon has five diagonals.  How many diagonals does a convex decagon have?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the number of diagonals in a convex decagon, we first need to understand the formula for calculating the number of diagonals in any convex polygon. The formula is given by:

D = n(n - 3) / 2

where D is the number of diagonals and n is the number of sides of the polygon.

In this case, we have a decagon, which has 10 sides. We will substitute n = 10 into the formula.

First, we calculate n - 3:

10 - 3 = 7

Next, we multiply n by (n - 3):

10 * 7 = 70

Now, we divide this product by 2 to find the number of diagonals:

70 / 2 = 35

Thus, the number of diagonals in a convex decagon is 35.<|END_OF_LATENT|> The final answer is $35$.