Mathematics

If the sides of a triangle are produced, then the sum of the exterior angle i.e. $$\angle a+\angle b+\angle c$$ is equal to


ANSWER

$${ 360 }^{ 0 }$$


SOLUTION
In $$\triangle ABC$$,
$$\angle a = \angle ABC + \angle ACB$$ (Exterior angle property)
$$\angle b = \angle ACB + \angle BAC$$ (Exterior angle property)
$$\angle C = \angle ABC + \angle BAC$$ (Exterior angle property)

Adding all the equations:
$$\angle a + \angle b + \angle c = 2 (\angle ABC + \angle ACB + \angle BAC)$$
$$\angle a + \angle b + \angle c = 2 (180)$$
$$\angle a + \angle b + \angle c =  360^{\circ}$$
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