4. In Fig. 6.16, if x+y = w+z, then prove that AOB is a line.
Solution: For proving AOB is a straight line, we will have to prove x+y is a linear pair i.e. x+y = 180° We know that the angles around a point are 360° so, x+y+w+z = 360° In the question, it is given that, x+y = w+z So, (x+y)+(x+y) = 360° 2(x+y) = 360° ∴ (x+y) = 180° (Hence proved).
