Question

18 Prove that if a ray stands on a line then the sum of the adjacent angles so formed is 180°​

Answer 1

Step-by-step explanation:

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.

Answer 2

$\huge\underline\mathfrak{\red{✨ANSWER✨}}$

When a ray stands on a line, two adjacent angles are formed. ... The two angles being adjacent, make a total angle of 180° on the straight line. Another way, we can see since the ray stands on the straight line, we can consider it is a perpendicular line. Thus, the two adjacent angles are right angles.