Question

prove that the Ray stands on a line , then the sum of two adjacent angle so formed is 180°​

Answer 1

Answer:

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°

Step-by-step explanation: