In $\triangle A B C, \angle A=88^{\circ}$. If I is the incentre of the triangle, then the measure of $\angle B I C$ is:

134°

We know incentre is a meet point of all the angle bisectors

So, \(\angle\)BIC = \({90}^\circ\) + \(\frac{A}{2}\)

⇒ \(\angle\)BIC = \({90}^\circ\) + \(\frac{88}{2}\)

⇒ \(\angle\)BIC = \({90}^\circ\) + \({44}^\circ\)

⇒ \(\angle\)BIC = \({134}^\circ\)

Therefore, \(\angle\)BIC = \({134}^\circ\).