Question

If one of the angles of a triangle is $110°$, then the angle between the bisectors of the other two angles is

• A. $70°$
• B. $110°$
• C. $35°$
• D. $145°$

Answer 1

The correct option is D

$145°$

Find both unknown angles.

Since, we know that the sum of angles of a triangle is $180°$.

So, sum of other two angles is

$\Rightarrow 180°-110°=70°$.

Both the angles get halved,

$\Rightarrow \frac{70°}{2}=35°$.

So, the third angle will be

$\Rightarrow 180°-35°=145°$.

Hence, $\mathrm{Option}\left(\mathrm{D}\right)$ is correct.