Step 1: Read the data.
The diploid chromosome number of the angiosperm is $2n = 36$, and we want the chromosome number of its endosperm.
Step 2: Recall how endosperm forms.
In angiosperms the endosperm comes from triple fusion during double fertilization.
Step 3: Understand triple fusion.
One haploid male gamete ($n$) fuses with the diploid secondary nucleus ($2n$), giving a triploid ($3n$) cell that becomes endosperm.
Step 4: Find the haploid number.
Since $2n = 36$, the haploid number is $n = \frac{36}{2} = 18$.
Step 5: Compute the triploid number.
Endosperm is $3n = 3 \times 18 = 54$.
Step 6: Conclude.
So the endosperm has $54$ chromosomes, which is option (4).
\[ \boxed{54} \]