The remote interior angles of a triangle are basically the two angles that do not share a vertex with and are opposite to the exterior angle.
5. ∠1 and ∠2
6. ∠2 and ∠3
7. ∠1 and ∠3
Because the exterior angle of a triangle is equal to the remote interior angles we can set up the following equations:
8.

9.
For this case we have that by definition, the density is given by:

Where:
M: It is the mass of the diamond
V: It is the volume of the diamond
According to the data of the statement we have:

So the volume is:

Thus, the volume of the diamond is approximately 
Answer:

the prime factorization is 99