Question

ABCDE is a Pentagon. Find angle A+B+C+D+E​

Answer 1

Step-by-step explanation:

Given,

pentagon ABCDE ,

Perimeter of ABCDE = 21cm

AB = 3cm

BC = x-y

CD = x+y

AE = 3cm

BE = 5cm

BE||CD, BC||DE, BC is perpendicular to CD

So, opp. sides are equal!

CD = BE

x+y = 5 ------- (1)

BC = DE = x-y

Now,

AB+BC+CD+DE+AE = 21

3+x-y+x+y+x-y+3 = 21

3x-y+6 = 21

3x-y = 21-6

3x-y = 15 -------- (2)

Now add (1) and (2)

3x-y+x+y = 15+5

4x = 20

x = 20/4

x = 5

Substitute x value in (2)

3x-y = 15

3(5)-y= 15

15-y = 15

-y = 15-15

-y = 0

y = 0

Therefore, x = 5 & y = 0

Answer 2

Answer:

108°

Step-by-step explanation:

sum of all angle=

(5 -2)×180°/5

=3×180°/5

=108°