Question

In ∆ABC, angle ABC= angle ACB. If the side BC is produced both ways. Prove that the exterior angles are equal.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

GIVEN: ∠ABC = ∠ACB

              Line BC has produced both ways

TO PROVE: Exterior Angles are equal.

                    ∠ABD = ∠ACE

SOLUTION:

In the figure,

∠ABD + ∠ABC = 180°                    (Linear Pair)          

      ∠ABD        = 180° - ∠ABC                       -------- Eq 1

Similarly,

∠ACB + ∠ACE = 180°                    (Linear Pair)          

      ∠ACE        = 180° - ∠ACB                       -------- Eq 2

Now,

Taking Eq 1,

   ∠ABD        = 180° - ∠ABC

    ∠ABD        = 180° - ∠ACB  ---- Eq 3       (Since, ∠ACB  =  ∠ABC )(Given)

Solving Eq 2 and Eq 3,

We get,

               ∠ABD = ∠ACE

                  Hence Proved.

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