Question

prove that if a ray stands on a straight line then then sum of two adjacent angels is 180digrees ​

Answer 1

Answer:

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Step-by-step explanation:

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

To prove: ∠AOC+∠BOC=180  o  

Construction: Draw a ray OE⊥AB.

Proof: ∠AOC=∠AOE+∠EOC ....(1)

∠BOC=∠BOE−∠EOC ....(2)

Adding equation 1 and 2

∠AOC+∠BOC=∠AOE+∠EOC+∠BOE−∠EOC

⇒∠AOC+∠BOC=∠AOE+∠BOE

⇒∠AOC+∠BOC=90 o  +90  o

(OE⊥AB)

⇒∠AOC+∠BOC=180  o

 

Hence, proved.