Question

find the value of angle A + Angle B + angle C + angle D + angle of the following figure

Answer 1

sum of all angles of a polygon of equals (n-2) × 180.


Have a look at the attachment and let those angles in a pentagon inside be a,b,c,d and e .



Now as the no. of sides in a pentagon = 5

Therefore , the sum of all angles in a pentagon = (5-2) 180°
= 3 × 180°
= 540°


Therefore,

a+b+c+d+e = 540° ----(vi)


Now,

In triangle AJC

an. A + an. C + a = 180° ----(i)

similarly in triangle DFB

an. D + an. B + b = 180° ------(ii)

In triangle EGC

an.E + an. C + c = 180° ------(iii)

In triangle AHD

an. A + an. D + d = 180° ------(iv)

In triangleEIB

an. E + an. B + e = 180° ------(v)



Add (i), (ii), (iii), (iv) and (v)

2 ( an. A + an. B + an. C + an. D + an.E ) + a+b+c+d+e = 900°


Using (vi)

2 (an. A + an.B + an. C + an.D + an. E ) + 540° = 900°


2 (an. A + an.B + an. C + an.D+ an.E ) = 900°-540°= 360°

an. A + an.B + an. C + an.D + an. E = 360°/2 = 180°.


Therefore,

angle A + angle B + angle C + angle D + angle E = 180° .

Answer 2

Answer:

Step-by-step explanation: