Question

"The measure of an exterior angle of a triangle is equal to the sum
of its remote interior angles". Prove the theorem.
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Answer 1

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.) FACTS: An exterior ∠ is equal to the addition of the two Δ angles not right next to it.

Answer 2

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

For example, in a triangle ABC,

 d = b + a

 e = a + c

 f = b + c

==> d + e + f = b + a + a + c + b + c

d + e + f = 2a + 2b + 2c

=2(a +b + c)

But according to triangle angle sum theorem,

a + b + c =180 degrees

therefore, d + e + f = 2(180 degree)

== 360degree

Hence it is proved