Question

to prove that the sum of all angle formed on the same side of a line at a point is 180

Answer 1

Heya,

In ∆ABC,

Here line l  | | m 

We take AB as transversal line and get

1  = BAC                                      ----- ( 1 )     ( Alternate interior angles )

And

Take AC as transversal line and get

2  = BCA                                      ----- ( 2 )     ( Alternate interior angles )


And,

BAC  + ABC +  BCA  =  180                      
(Sum of all internal angles of triangle is 180 )

Substitute values from equation 1 and 2 and get

ABC +   1  + 2 =  180

So, We can say Sum of these angle is a straight line ( l )                        HENCE PROVED!

HOPE IT HELPS:-))