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Question

# (a) Find the sum of all the exterior angles of a triangle. (b) Is there a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm? [4 MARKS]

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Solution

## (a) Solution: 1 Mark Correct answer: 1 Mark (b) Reason: 1 Mark Correct answer: 1 Mark (a) 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°. (b) Suppose such a triangle is possible. Then the sum of the lengths of any two sides would be greater than the length of the third side. Let's check this. Is 4.5 + 5.8 > 10.2? Yes Is 5.8 + 10.2 > 4.5? Yes Is 10.2 + 4.5 > 5.8? Yes Therefore, the triangle is possible.

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