Question

In the figure, which of the following statements must be true?
(i)a+b=d+c (ii)a+c+ e = ${180}^0$
(iii) b+f=c+e

• A. (ii) and (iii) only
• B. (i) only
• C. (ii) only
  
• D. (iii) only

Answer 1

Answer: (A)

In the figure, a = d
b = e
c = f (Vertically opposite angles)

(i) From the given relations, we can see that a+b is not equal to d+c.

(ii) a + b + e = ${180}^0$
a + e + c ${180}^0$
$\Rightarrow a+c+e={180}^0$
(iii) b + f= e+ c
$\therefore$ (ii) and (iii) are true statements.