Mathematics

The angle between the internal and the external bisectors of an angle of a triangle is ___________.


ANSWER

$$90^o$$


SOLUTION

Let's say an angle of a triangle is $$\theta$$, then after it is bisected each smaller angle will now be $$\dfrac{\theta}{2}$$.

If you take the external angle of $$\theta$$, it will be $$180^o-\theta$$ and if this is bisected the two new angles would be $$\dfrac{(180^o-\theta)}{2}$$ which is equal to $$\dfrac{90^o - \theta}{2}$$.

Now adding these two angles, we get $$\dfrac{\theta}{2} + \dfrac{90^o - \theta}{2} = 90^o$$.

Hence the angle between the internal and external bisectors of an angle of a triangle is always $$90^o$$.

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