Question : If the sides of a triangle are extended on both sides then the sum of the exterior angles formed on both sides is:
Option 1: $360^{\circ}$
Option 2: $540^{\circ}$
Option 3: $720^{\circ}$
Option 4: $180^{\circ}$
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Correct Answer: $720^{\circ}$
Solution :
$\angle$ABC + $\angle$BCA + $\angle$BAC = $180^{\circ}$ ---------------(i)
⇒ $\angle$ACB + $\angle$ACD = $180^{\circ}$ ---------------(ii)
⇒ $\angle$ABC + $\angle$ABF = $180^{\circ}$ ---------------(iii)
⇒ $\angle$BAC + $\angle$EAC = $180^{\circ}$ ---------------(iv)
Adding (ii), (iii), and (iv), then subtracting (i) from it,
$\therefore$ $\angle$ACD + $\angle$ABF + $\angle$EAC = $540^{\circ}$ – $180^{\circ}$ = $360^{\circ}$
So, the sum of the exterior angles formed on both sides = $2 × 360^{\circ}$ = $720^{\circ}$
Hence, the correct answer is $720^{\circ}$.
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