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The sum of all exterior angles of a triangle is:

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180°

360°

540°

720°

answer is B.

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Detailed Solution

We need to find the sum of all exterior angles of a triangle.
Let us consider a triangle with its exterior angles as follows,
Question Image

Now, we know that a pair of an exterior and interior angle at a location is always supplementary.
Using this fact, we can express the exterior angles of the triangle in terms of its interior angles as follows,

p + x = 180 ∘ p = 180 ∘ − x ........ (i) q + y = 180 ∘ q = 180 ∘ − y ........ (i i) r + z = 180 ∘ r = 180 ∘ − z ......... (i i i)

Adding the equations (i), (ii) and (iii), we get,

p + q + r = 180 ∘ − x + 180 ∘ − y + 180 ∘ − z p + q + r = 540 ∘ − x − y − z p + q + r = 540 ∘ − (x + y + z) ......... (i v)

Now, from the angle sum property of a triangle, we have, the sum of its interior angles as,

x + y + z = 180 ∘

Using this in the equation (iv), we get,

p + q + r = 540 ∘ − 180 ∘ p + q + r = 360 ∘

From the equation, it is clear that the sum of all the exterior angles of a triangle is

360 °

.
Hence, the correct option is (2).

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