Question

If x+y = w+y ,thenprove that AOB is a line​

Answer 1

Answer:

answer for the given problem is given

Answer 2

To prove that AOB is a line, we need to prove that ∠x + ∠y = 180°.

(Applying Axiom 6.2)

Axiom Used: If the sum of two adjacent angles is 180° then the non-common arms of the angles form a line.

[Here the common arm is OC, and the non-common arms are AO & BO]

From the figure;

(Angles around a point (O) adds up to 360°)

⇒ x + y + z + w = 360°

But we've been given that x + y = w + z. Therefore;

⇒ w + z + z + w = 360°

⇒ 2w + 2z = 360°

⇒ 2(w + z) = 360°

⇒ w + z = 360°/2

⇒ w + z = 180°

ATQ; x + y = w + z

∴ x + y = w + z = 180°

Applying the Axiom mentioned previously here, we can conclude that AOB is a line.