Answer
Verified
350.7k+ views
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 $ \angle DFE $ ) is equal to $ {36^ \circ } $
The inner angles of the pentagram (angles of the pentagon) are of $ {108^ \circ } $
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 $ \angle DFE $ ) is equal to $ {36^ \circ } $
The inner angles of the pentagram (angles of the pentagon) are of $ {108^ \circ } $
Recently Updated Pages
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Advantages and disadvantages of science
10 examples of friction in our daily life
Trending doubts
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Who was the first to raise the slogan Inquilab Zindabad class 8 social science CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
One cusec is equal to how many liters class 8 maths CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
A resolution declaring Purna Swaraj was passed in the class 8 social science CBSE