Question

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

1 point



(a) 360°

(b) 108°

(c)180°

(d) 216°​

Answer 1

Step-by-step explanation:

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

n - 360°

, n= number of sides

Here for pentagon, Each interior angle=180°

360° - 5

=108°

From figure in ΔABE−

A=108°

And, ∠ABE=∠AEB since AB=AE

⟹∠ABE+∠AEB+∠A=180°

⟹∠ABE+∠AEB+108°

=180°

⟹∠ABE=∠AEB=36°

Hence,a=36°

Similarly from ΔBCD−

∠CBD=∠CDB=36°

Now ∠CBA=∠ABE+∠EBD+∠CBD

⟹108°

=36°

+∠EBD+36°

⟹∠EBD=b=36°

Now in ΔBCD−

∠CDE=∠CDB+c

⟹108°

=36°

⟹c=72°

Hence c=2a=2b where b=36°

Answer 2

Answer:

b) 108

Step-by-step explanation:

the sum of all the interior angles of a pentagon is 540

and a pentagon has 5 sides

so, 540÷5 = 108