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What is the sum of all exterior angles of a triangle?

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360^{o}

180^{o}

540^{o}

None of these

answer is A.

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Detailed Solution

We need to find the sum of all exterior angles of a triangle.
Let the angles of the triangle be x,y, and z.
By angle sum property,

x + y + z = 180^{\circ}

x + y = Exterior angle A

y + z = Exterior angle B

x + z = Exterior angle C

Sum of exterior angles = x + y + y + z + x + z

\Rightarrow Sum of exterior angles = 2 x + 2 y + 2 z

\Rightarrow Sum of exterior angles = 2 \times 180^{\circ}

\Rightarrow Sum of exterior angles = 360^{\circ}

The sum of all exterior angles of a triangle is

360^{o}

.
Hence, the correct option is 1.

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