Question

in the figure , if x+y=w+z then prove that AOB is a line​

Answer 1

Given :

• x + y = w + z

To Prove :

• AOB is a line .

Solution :

As we know that :

$\longmapsto\tt{x+y+z+w=360\degree\:(Complete\:Angle)}$

$\longmapsto\tt{w+z+z+w=360\degree}$

$\longmapsto\tt{2w+2z=360\degree}$

$\longmapsto\tt{2(w+z)=360\degree}$

$\longmapsto\tt{w+z=\cancel\dfrac{360}{2}}$

$\longmapsto\tt\bf{w+z=180\degree}$

HENCE PROVED

_______________________

Angle :

When two rays originate from the same end point , they form an angle .

Collinear Point :

If three or more than three points lie on the same line they are called as Collinear Points .

Linear Pair of Angles :

Two adjacent angles whose sum is 180° is called as Linear Pair of Angles .

_______________________

Answer 2

GIVEN THAT:-

$\large\sf\purple{x+y=w+z}$

WE KNOW THAT:-

$\large\sf\green{x+y+w+z=360°}$

$\large\sf\green{x+y+x+y=360°}$

$\large\sf\green{2(x+y)=360°}$

$\large\sf\green{x+y=180°}$

$\therefore$$\huge\tt\underline\red{AOB\:is\:a\:line}$