In ΔABC, ∠A = 68°. If I is the incentre of the triangle, then the measure of ∠BIC is:

124°

According to the concept

\(\angle\)BIC = \({90}^\circ\) + \(\frac{1}{2}\) x \(\angle\)BAC

\(\angle\)BIC = \({90}^\circ\) + \(\frac{1}{2}\) x \({68}^\circ\)

\(\angle\)BIC = \({90}^\circ\) + \({34}^\circ\)

\(\angle\)BIC = \({124}^\circ\)

Therefore, \(\angle\)BIC is \({124}^\circ\)