Question

prove that the measure of an exterior angle of triangle is equal to the sum of its remote interior angles​

Answer 1

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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

For a given triangle, sum of the three angles =

180

0

As per the diagram,

∠1+∠2+∠3=180°

AD is a straight line and CB stands on it.

Therefore, angle 2 and angle 4 are supplementary.

I.e.

∠2+∠4=180°

Hence

∠1+∠2+∠3=∠2+∠4

∴∠1+∠3=∠4

In other words, exterior angle is equal to sum of the two interior opposite (remote) angles.

Similarly, we can prove the other 5 exterior angles