As Given, x+y=w+zTo Prove: AOB is a line or x+y=180∘ (linear pair.)According to the question,x +y+w+z=360∘ ∣ Angles around a point.(x+y)+(w+z)=360∘(x+y)+(x+y)=360∘ ∣ Given x+y=w+z2(x+y)=360∘(x+y)=180∘Hence, x+y makes a linear pair. Therefore, AOB is a straight line.