Question

In fig.6.16 if x+y=w+z ,then prove that AOB is a line.

Answer 1

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◾◾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______❤

✿┅═══❁✿ Be Brainly✿❁═══┅✿

Answer 2

$\huge\star{\red{\underline{\underline{\mathbb{EXPLANATION:}}}}}$

______________________________

Given that:-

• x+y=w+z

To prove:-

• AOB is a line

For proving AOB is a straight line, we will have to prove x + y is a linear pair

i.e. x + y = 180°

We know that the angles around a point are 360° so,

$\mapsto$x + y + w + z = 360°

In the question, it is given that,

$\mapsto$x + y = w + z

So, (x + y) + (x + y) = 360°

=> 2(x + y) = 360°

∴ (x + y) = 180°

$\tt{\red{\underline{\star{Hence\:proved!}}}}$