Question

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

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Solution

## (a) Steps: 1 Mark Correct answer: 1 Mark (b) Reason: 1 Mark Correct answer: 1 Mark (a) In the figure, 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+∠3=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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