Question

show that the exterior angle of a triangle is equal to the sum of two opposite interior angle

Answer 1

in a triangle..

angle 1 + 2 + 3 =180..

angle 3 +4 = 180 (linear pair)

1 + 2 +3 = 3 +4

1 +2 =4 .

Answer 2

aloha user!
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given: triangle ABC
to prove: angle A + angle B = angle ACD
proof:we know that the sum of angles of a triangle is 180°.
also angle ACD and angle ACB form a straight angle.
so,
angle ACD + angle ACB = 180°.------(1)
angle A + angle B + angle ACB = 180°-------(2)

as (1) and (2) are equal we can write:

angle ACD + angle ACB = angle A + angle B + angle ACB

( angle ACB - angle ACB = 0 )

angle ACD = angle A + angle B

hence proved.
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hope it helps :^)