Question

How many triangles in a pentagram?

Answer 1

Hint: A pentagram which is also sometimes known by different names such as pentalpha, or star pentagon is the shape of a five-pointed polygon star. We will draw the figure of a pentagram and then try to count its number of triangles and then get our final answer.

Complete step-by-step answer:
A pentagram is in the shape of a five pointed polygon star, A figure of a pentagram is given below

There are five sides of the pentagram given above in the figure, the sides are namely,
 $FH,FI,JG,JH,IG$
The five sides overlap and cut each other to form a pentagonal star. The figure in middle $ABCDE$ is the pentagon. We have to tell the number of triangles which are in the given figure. There are $10$ isosceles triangles as each side of the pentagonal star is equal.
The triangle are,
 $FDE,JCD,IBC,HAB,GEA$ these are the triangles which are acute angle triangles. The other five obtuse angle triangles are listed below,
 $CFH,BJG,AIF,EHJ,DGI$
These are obtuse angle triangles thus in total we have $10$ triangles (all isosceles) in a pentagram of which $5$ are acute angled triangles and the rest are obtuse angled triangles.

Note: Some other facts about a pentagram,
A pentagram has $10$ vertices. Five are the outer vertices of the star tips, the other five vertices are the vertices of the inner pentagon.
Each outer angle of the pentagram (For example $\mathrm{\angle }DFE$ ) is equal to ${36}^{\circ }$
The inner angles of the pentagram (angles of the pentagon) are of ${108}^{\circ }$