Question

3.
Given that ABCDE is a regular polygon, find the measure of x, y and z.
A
Х
у
E
B
х
Z
D
С​

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