If the sides of a triangle are produced in an order, show that the sum of the exterior angles so formed is 360°.
Solution:
Given, the sides of a triangle are produced in an order.
We have to show that the sum of the exterior angles so formed is 360°.
Consider a triangle ABC,
Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.
∠A + ∠B + ∠C = 180°
AB, BC and CA are produced to F, D and E.
Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.
From the figure,
The exterior angle are ∠1, ∠2 and ∠3.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.
∠3 = ∠A + ∠C
∠1 = ∠A + ∠B
∠2 = ∠B + ∠C
Sum of exterior angles = ∠1 + ∠2 + ∠3
= (∠A + ∠C) + (∠A + ∠B) + (∠B + ∠C)
= ∠A + ∠A + ∠B + ∠B + ∠C + ∠C
= 2(∠A + ∠B + ∠C)
= 2(180°)
= 360°
Therefore, the sum of the exterior angles is 360 degrees.
✦ Try This: Rani takes the shortest route to her home by walking diagonally across a square park. The park measures 60 metres. How much shorter is the route across the park than the route around its edges?
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 123
If the sides of a triangle are produced in an order, show that the sum of the exterior angles so formed is 360°.
Summary:
If the sides of a triangle are produced in an order, it is shown that the sum of the exterior angles so formed is 360°.
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