Math, asked by sunilsaha9331282348, 5 hours ago

Given ABCDE is a regular pentagon, then sum of <A and <B=________ *

1 point



(a) 360°

(b) 108°

(c)180°

(d) 216°​

Answers

Answered by khushbutripathi1986
1

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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