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Question

Question 123

If the sides of a triangle are produced in an order, show that the sum of the exterior angles so formed is 360

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Solution

In ΔABC, by exterior angle property,
Exterior 1= Interior A + Interior B) ....... (i)
Exterior 2= Interior B + Interior C ....... (ii)
Exterior 3= Interior A + Interior C ....... (iii)

On adding Eqs. (i), (ii) and (iii), we get
1+2+3=2(A+B+C)
[by angle sum property of a triangle, A+B+C=180]
1+2+3=2×1801+2+3=360
Hence, the sum of exterior angles is 360


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