In triangle ABC, $\angle A = 70^\circ$. The bisectors of $\angle B$ and $\angle C$ meet at I. What is $\angle BIC$?

Explanation

1. 01

   $\angle B + \angle C = 180^\circ - 70^\circ = 110^\circ$, so half of each together = 55°.

2. 02

   In triangle BIC, $\angle BIC = 180^\circ - 55^\circ = 125^\circ$.

3. 03

   Shortcut: $\angle BIC = 90^\circ + \frac{1}{2}\angle A = 90^\circ + 35^\circ = 125^\circ$.