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Question

Find the sum of all the exterior angles of a triangle. [4 MARKS]

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Solution

Visualizing the question and respective diagram : 1 Mark
Properties : 1 Mark
Steps : 1 Mark
Result : 1 Mark

In the above figure shown, 1, 2 and 3 are the interior angles whereas 4, 5 and 6 are exterior angles. Using linear pair axiom, we can say that:
1 + 4 = 180
°

3 + 6 = 180°

2 + 5 = 180°

Adding all of them, we get:

(1 + 4) + (3 + 6) + (2 + 5) = 540°

Rearranging the terms, we get:

(1 + 2 + 3) + (4 + 5 + 6) = 540°

1 + 2 + 3 = 180° (Angle Sum Property of a triangle)

So, (4 + 5 + 6) = 540° - 180° = 360°

So, the sum of the exterior angles of a triangle is 360°.


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