Question

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

Answer 1

$\large{\boxed{\bold{Answer:}}}$

$x + y = w + z \: \: \: ...(1)$
Sum of angles round a point is 360°

$x + y + w + z \: = 360° \\ \\ = > x + y + x + y = 360° \\ \\ = > 2(x + y) = 360° \\ \\ = > x + y = \frac{360}{2} \\ \\ = > x + y \: = 180°$

Therefore, AOB is a line

(If the sum of two adjacent angles is 180° then the non- common arms of angles form a line)

$\large{\boxed{\bold{Hope\:it\:helps\:you!}}}$

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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