Question

in the given figure side BC of triangle ABC is produced in both the directions . prove that the sum of the two exterior angles so formed is greater than 180°

Answer 1

in triangle ABC 
angle ABE = angle BAC + angle BCA      (exterior angle is equal to the sum of                                                                                 two opposite angles)
angle ACD = angle BAC + angle CBA       (same reason as above)
when,  angle BAC + BCA + CBA =180       (angle sum property)
then,  angle (BAC + BCA ) + angle (BAC + CBA )  < 180 
so, angle ABE + angle ACD will be greater than 180

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