Question

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

• A. ${90}^o$
• B. ${180}^o$
• C. ${270}^o$
• D. ${30}^o$

Answer 1

The correct option is A ${90}^o$

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

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 $\frac{({180}^o-\theta )}{2}$ which is equal to $\frac{{90}^o-\theta }{2}$.

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

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