Question

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

Answer 1

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For a given triangle, sum of the three angles =

180°

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.

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