Question

If the vertical angle of a triangle is 130°, then the angle between the bisectors of the base angles of the triangle is
(a) 65°
(b) 100°
(c) 130°
(d) 155°

Answer 1

(d) 155°



Let ABC be a triangle and let $\angle A=130°$.
Then, from $∆ABC$, we have:
$$\begin{gathered} \angle A+\angle B+\angle C=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 130°+\angle B+\angle C=180° \\ \Rightarrow \angle B+\angle C=50° \\ \Rightarrow \frac{1}{2}\angle B+\frac{1}{2}\angle C=25°...\left(i\right) \end{gathered}$$

Now, in $∆BOC$, we have:
$$\begin{gathered} \frac{1}{2}\angle B+\frac{1}{2}\angle C+\angle BOC=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 25°+\angle BOC=180°\left[\text{Using}\left(i\right)\right] \\ \Rightarrow \angle BOC=155° \end{gathered}$$