Question

prove that the measure of an exterior angle of a
triangle is equal to the sum of its remore interion
Angles.( step by step answer) ​

Answer 1

ANSWER

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.

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Answer 2

Given :- ∆ABC, AB is produced to D, where angle CBD is the exterior angle.

To prove :- angle 1 + angle 3 = angle 4

Proof :- From given ∆ABC,

Sum of the three angles = 180°

As per the diagram,

angle 1 + angle 2 + angle 3 = 180° ...(1)

Now, CB is perpendicular to AD by construction.

Therefore angle 2 and angle 4 are supplementary.

i.e. angle 2 + angle 4 = 180° .....(2)

equating equation (1) & (2),

angle 1 + angle 2 + angle 3 = angle 2 + angle 4

therefore, angle 1 + angle 3 = angle 4