DRAW THE FIG LIKE THIS- in tringle ABC, let angle A be the vertical angle and angle B and C be the base angles.

GIVEN: Triangle ABC

TO PROVE:ANGLE A+ANGLE B+ANGLE C=180

CONSTRUCTION:Through A,draw DA parallel to BC

then, angle DAB= angle ABC(ALTERNATE INTERIOR ANGLES)----------(1)

angle EAC= angle ACB( ALTERNATE INTERIOR ANGLES)-----------------(2)

Now,

angle DAB+ angle EAC+ANGLE BAC=180(THE SUM OF THE ANGLES ON A STRAIGHT LINE IS 180)

=ANGLE ABC+ANGLE ACB+ANGLE BAC=180(FROM EQUATION 1 2 ,ANGLE DAB=ANGLE ABC ANGLE EAC=ANGLE ACB)

HENCE, IN TRINGLE ABC, ANGLE A +ANGLE B +ANGLE C=180

HENCE PROVED.