Question

in fig. 6.16, if x+y=w+z, then prove that AOB is a line.

Answer 1

hope my answer helps you ✌

please refer this attachment .

Answer 2

Since sum of the all the angles round a point is equal to 360°.

Therefore,

                    x + y + w + z = 360°

             ⇒ (x + y) + (w + z) = 360°

             ⇒ (x + y ) + (x + y) = 360°  [∵  x + y = w + z]

             ⇒ 2(x + y) = 360°

             ⇒ x + y = 360/2

             ⇒ x + y = 180°

          ⇒ AOB is a straight line.

HOPE IT HELPS ...