Question

In Fig. 6.16, if x + y=w+z, then prove that AOB is a line. B x D W Z A Fig. 6.16 ​

Answer 1

Answer:

we know that

x + y + w + z = 360°

(x+y) + (w+z) = 360°

(x+y) +(x+y) = 360°

2(x+y) = 360°

(x+y)= 360°/2

x+y = 180°

Since,

w+z = x+y

w+z = 180°

Now,

x + y = 180° and w + z = 180°

we know that if sum of of two adjacent angles is 180° then non - common arms form a line ( Reverse linear Pair)

•°• AOB is a straight line

Hence , Proved