Question

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

Answer 1

☄️ Question :-

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

☄️ Solution :-

We know that,

$\mapsto \bf x + y + w + z = 360°$

[Sum of all the angles at a point=360°]

$\mapsto \bf (x+y)+(w+z)=360°$

$\mapsto \bf (x+y)(x+y)=360°\:\:[Given, \:x+y=w+z$

$\mapsto \bf 2(x+y)=360°$

$\mapsto \bf x+y=\dfrac{360°}{2}$

$\mapsto \bf x+y=180°$

Since,$\bf w+z=x+y$

$\mapsto \bf w+z=180°$

$\bf Now, \:x+y=180°\:and\:w+z=180°$

⭐From axiom 6.2 : If the sum of two adjacent angles is 180°, then non-common arms form a line [Reverse linear pair].

_________________________

Therefore, AOB is a straight line.

Hence, proved !!

Answer 2

Answer:

We know that,

\mapsto \bf x + y + w + z = 360°↦x+y+w+z=360°

[Sum of all the angles at a point=360°]

\mapsto \bf (x+y)+(w+z)=360°↦(x+y)+(w+z)=360°

\mapsto \bf (x+y)(x+y)=360°\:\:[Given, \:x+y=w+z↦(x+y)(x+y)=360°[Given,x+y=w+z

\mapsto \bf 2(x+y)=360°↦2(x+y)=360°

\mapsto \bf x+y=\dfrac{360°}{2}↦x+y=

2

360°

\mapsto \bf x+y=180°↦x+y=180°

Since,\bf w+z=x+yw+z=x+y

\mapsto \bf w+z=180°↦w+z=180°

\bf Now, \:x+y=180°\:and\:w+z=180°Now,x+y=180°andw+z=180°

⭐From axiom 6.2 : If the sum of two adjacent angles is 180°, then non-common arms form a line [Reverse linear pair].

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