CBSE Class 9 Answered

Consider a triangle ABC.

To prove, angle a + angle b + angle c = 180 degrees

Through vertex A, draw a line l parallel to BC.

Since alternate interior angles are equal so;

Angle b = angle x                     … (1)

Angle c = angle y                      … (2)

Since l is a straight line so, angle x + angle b + angle y = 180 degrees

Therefore, angle b + angle a + angle c = 180 degrees    [Using (1) and (2)]

That is angle a + angle b + angle c = 180 degrees

Hence, proved.