If Fig. if x + y = w + z, then prove that AOB is a line.

1.	If Fig. if x + y = w + z, then prove that AOB is a line.
Answer» Data: In this fiure, ∠BOC = x° ∠AOC = y° ∠BOD = w° ∠AOD = z° and x + y = w + z. To Prove: AOB is a straight line. Proof: x + y + w + z = 360° (∵ one completre angle) But, x + y = w + z. ∴ x + y = w + z= \(\frac{360}{2}\) = 180° ∴ x + y = 180° ∴ w + z = 180° proved. But, ∠AOC and ∠BOC are adjacent angles, ∠AOC + ∠BOC = 180° x = y = 180° ∴ ZAOB = 180°. ∴ AOB is a straight line.

Answer»

Data: In this fiure, ∠BOC = x°

∠AOC = y° ∠BOD = w°

∠AOD = z° and x + y = w + z.

To Prove: AOB is a straight line.

Proof: x + y + w + z = 360°

(∵ one completre angle)

But, x + y = w + z.

∴ x + y = w + z= \(\frac{360}{2}\) = 180°

∴ x + y = 180°

∴ w + z = 180° proved.

But, ∠AOC and ∠BOC are adjacent angles,

∠AOC + ∠BOC = 180°

x = y = 180°

∴ ZAOB = 180°.

∴ AOB is a straight line.

Discussion