Question

Prove that the external angle of a triangle is the sum of the opposite internal angles.

Note:-
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Answer 1

In the given figure, the side BC of ∆ABC is extended. The exterior angle ∠ACD so formed is the sum of measures of ∠ABC and ∠CAB.

Proof:

From figure 3, ∠ACB and ∠ACD form a linear pair since they represent the adjacent angles on a straight line.

Thus, ∠ACB + ∠ACD = 180° ……….(2)

Also, from the angle sum property, it follows that:

∠ACB + ∠BAC + ∠CBA = 180° ……….(3)

From equation (2) and (3) it follows that:

∠ACD = ∠BAC + ∠CBA

Answer 2

The term happiness is used in the context of mental or emotional states, including positive or pleasant emotions ranging from contentment to intense joy.

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