Question

7 The following figure is a combination of a regular pentagon and a squre find {abc​

Answer 1

Answer:

We know that each interior angle of a regular polygon is given by 180  

o

−  

n

360  

o

 

​

 , n= number of sides

Here for pentagon, Each interior angle=180  

o

−  

5

360  

o

 

​

=108  

o

 

From figure in ΔABE−

A=108  

o

 

And, ∠ABE=∠AEB  since AB=AE

⟹∠ABE+∠AEB+∠A=180  

o

 

⟹∠ABE+∠AEB+108  

o

=180  

o

 

⟹∠ABE=∠AEB=36  

o

 

Hence,a=36  

o

 

Similarly from ΔBCD−

∠CBD=∠CDB=36  

o

 

Now ∠CBA=∠ABE+∠EBD+∠CBD

⟹108  

o

=36  

o

+∠EBD+36  

o

 

⟹∠EBD=b=36  

o

 

Now in ΔBCD−

∠CDE=∠CDB+c

⟹108  

o

=36  

o

+c

⟹c=72  

o

 

Hence c=2a=2b where b=36  

o