(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]
(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]
(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.
(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.
