Question

Prove that If a ray stands on a line then the sum of the adjacent angles so formed is 180°.

Answer 1

Hey mate!

The answer is given below :

When a ray stands on a line, two adjacent angles are formed.

We know that the angle lying on a straight line is 180°.

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.

So, the total angle

= 90° + 90°

= 180°

(Referred to the given attachment.)

Answer 2

A ray CD stands on a line AB such that /_ACD and /_ BCD are formed.


To Prove : /_ ACD + /_ BCD = 180°



Construction : Draw CE Perpendicular AB.


Proof : /_ ACD = /_ ACE + /_ ECD ----(1)

And,

/_ BCD = /_ BCE - /_ ECD -------(2)


Adding (1) and (2) , we get :

/_ ACD + /_ BCD = ( /_ ACE + /_ECD ) + ( /_ BCE - /_ ECD ) = ( /_ ACE + /_ BCE ) = ( 90° + 90° ) = 180 [ Since /_ ACE = /_BCE = 90° ]


Hence,


/_ ACD + /_ BCD = 180°