Question

if x+y=w+z,then prove that AOB IS A LINE

Answer 1

{See the figure in the attachment}
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We know that,

Sum of all angles in a circle is equal to 360°.

∠AOC + ∠BOC + ∠DOB + ∠AOD = 360°

» x+y+w+z = 360°
» x+y+x+y = 360° {x+y = w+z)
» 2x+2y = 360°
» 2(x+y) = 360°
» x+y = 180°

x+y = w+z = 180°

As the sum of two adjacent angles is equal to 180° (linear pair), it is a straight line.

Therefore, 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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