Question

in the figure, AOB and COD are straight lines.If x+y+z=180,prove that EOF is a straight line.

Answer 1

Given, x+y+z=180

COB = AOD [ Vertically opposite angles]

AOD = z

AOE = BOF [ Vertically opposite angles]

BOF = x

EOC = DOF [ Vertically opposite angles]

EOC = y

AOD + BOF + EOC = 180°

Also, x + y + z = 180 °

AOE + AOD + DOF = x + z + y = 180°

Hence, it forms Linear pair.

So, EOF is a straight line.

Answer 2

Please see the attachment