Question

in the given figure if x+y = w+z

the prove that AOB is a line​

Answer 1

$\huge\bigstar\underline\mathfrak\pink{Explanation}$

$\large\underline\bold\blue{Given-}$

x + y = w + z

$\large\underline\bold\blue{To\:prove-}$

AOB is a straight line.

$\large\underline\bold\blue{proof-}$

We know that,

Angle w + Angle x + Angle y + Angle z = 360° [ complete angle ]________(i)

Also,

x + y = w + z ( given )

Now, put x + y = w + z in eq (i).

We get,

Angle x + Angle y + Angle x + Angle y = 360°

2 Angle x + 2 Angle y = 360°

2 ( Angle x + Angle y ) = 360°

Angle x + Angle y = 360°\2

Angle x + Angle y = 180°

_________________________

Now,

The two angles forms linear pair with the sum of 180°.

Hence, AOB is a straight line.

Answer 2

✯✯ QUESTION ✯✯

In the given Figure if $x+y = w+z$

The Prove that AOB is a line ..

✰✰ ANSWER ✰✰

$\longmapsto\tt{Given:.x+y=w+z}$

$\longmapsto\tt{To prove:.AOB\:is\:a\:line}$

➙Proof : -

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

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

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

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

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

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

✺ HENCE PROVED ✺