Question
(a) Find the sum of all the exterior angles of a triangle. Â
(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]
(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]
Answer:
:
(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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:
(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.
Was this answer helpful ?
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