Mathematics

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

$90^o$

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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Single Correct Medium Published on 09th 09, 2020
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