Question

If x+y=w+z then prove that AOB is a line

Answer 1

angle X + angle Y is equals to 180 degree (linear pair)
angle w + angle Z is equal to 180 degree(linear pair)

angle X + angle Y + angle w + angle Z is equals to 360 degree

(angle X + angle y)(angle w + angle Z) is equals to 360 degree

(angle X + angle y)(angle X + angle y) is equals to 360 degreE

2 angle X + 2 angle Y is equals to 360 degree

2(angle X + angle y) is equals to 360 degree

angle X + angle Y is equals to 360/2 is equals to 180 degree

angle X + angle Y is equal to 180 degrees

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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