A) A B C D E is a regular polygon. Find the measure of LBEC.
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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
Step-by-step explanation:
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