Question

if they raised and on a line then the sum of two adjacent angle formed 180 degree . prove it ! ​

Answer 1

Correct question

if a Ray stands on a line , then the sum of two adjacent angle formed 180° .

Answer

Given,

A ray LM stands on a line AB .

Such that angle ALM and angle BLN are formed .

To prove ,

angle ALM + angel BLN = 180° .

Construction ,

Draw ray LN parallel to AB .

Proof :

=>

$\angle \: aln \: = \angle \: alm \: + \angle \: mln \: ....(eq.1)$

=>

$\angle \: bln \: = \angle \: blm \: + \angle \: mln ....(eq.2)$

adding the equation 1 and equation 2 we get ;

$\angle \: aln \: + \angle \: nlb \: = \angle \: alm \: + \angle \: mln \: + \angle \: \: blm \: - \angle \: mln$

$= \angle \: alm \: + \angle \: blm$

$= > 90 \degree \: + 90 \degree \: = \angle \: alm \: + \angle \: blm$

$= > 180 \degree \: = \angle \: alm \: + \angle \: blm$

Hence, proved !

Answer 2

Correct Question :

If a Ray stands on a line , then the sum of two adjacent angle formed 180° .

Given :

A ray OC stands on line AB then, adjacent angle ∠AOC and ∠BOC are formed.

To Prove :

∠AOC + ∠BOC = 180°

Construction :

Draw a ray OE ⊥ AB

Proof :

∠AOC = ∠AOE + ∠EOC....(1)

∠BOC = ∠BOE - ∠EOC.....(2)

Adding Equations 1 and 2 :

∠AOC + ∠BOC = ∠AOE + ∠EOC + ∠BOE - ∠EOC

⇒∠AOC + ∠BOC = ∠AOE + ∠BOE

⇒∠AOC + ∠BOC = 90° + 90° (OE⊥AB)

⇒∠AOC + ∠BOC = 180°

Hence proved. ✅

$Hope-it-helps-u$