In Fig. 8.126, which of the following statements must be true?

(i) a + b = d + c

(ii) a + c + e =180°

(iii) b + f = c + e

Question

In Fig. 8.126, which of the following statements must be true? (i) a + b = d + c (ii) a + c + e =180&#xB0; (iii) b + f = c + e

Philoid · Accepted Answer

Let AB, CD and EF intersect at O

∠AOD = ∠COB (Vertically opposite angle)

b = e (i)

∠EOC = ∠DOF (Vertically opposite angle)

f = c (ii)

Adding (i) and (ii), we get

b + f = c + e (iii)

Now,

∠ADE + ∠EOC + ∠COB = 180^o

a + f + e = 180^o

a + c + e = 180^o [From (ii)]

In Fig. 8.126, which of the following statements must be true?(i) a + b = d + c(ii) a + c + e =180°(iii) b + f = c + e