Q. 2 E

# Sum of the three exterior angles of a triangle is __________

A. two right angles

B. three right angles

C. one right angle

D. four right angles

Answer :

We know that an exterior angle of a triangle is equal to the sum of the interior opposite angles.

⇒ ∠A + ∠B = external ∠C

∠A + ∠C = external ∠B

∠C + ∠B = external ∠A

Adding above three, we get

2∠A + 2 ∠B + 2∠C = sum of the three external angles

⇒ 2(∠A + ∠B + ∠C) = sum of the three external angles

We know that the sum of the angles of a triangle is 180°.

⇒ 2× 180° = sum of the three external angles

⇒ Sum of the three external angles = 4 × 90°

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