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प्रश्न
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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उत्तर
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 equations (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 × 180°
⇒ ∠1 + ∠2 + ∠3 = 360°
Hence, the sum of exterior angles is 360°.
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