Question

In the given figure, if x+y=w+z,then prove that AOB is a line.

Answer 1

x+y = w+z.

x+y+w+z = 360° ( complete angle)

x+y+x+y = 360°
2x + 2y = 360°
2(x+y) = 360°
x+y = 360°/2
x+y = 180°


SO, x+y is a linear pair and as we know linear pair forms only on an line SO,AOB is a line

Answer 2

☺ Hello mate__ ❤

◾◾here is your answer...

Given:  x+y=w+z             (1)

To prove: AOB is a line

Proof:    x+y+w+z=360°       (Sum of all angles around point=360°)

Putting (1) in the above equation, we get

x+y+x+y=360°

⇒2x+2y=360°

⇒x+y=360°/2=180°

Therefore, x and y form a linear pair

Hence, AOB is a straight line.

I hope, this will help you.

Thank you______❤

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