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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