In a ΔABC, the bisectors of ∠B and ∠C meet at O. If ∠BOC = 142°, then the measure of ∠A is:

104°

Let \(\angle\)B x and \(\angle\)C = y

OB and OC are two angle bisectors and meets at O

In \(\Delta \)BCO,

\(\frac{x}{2}\) + \(\frac{y}{2}\) + 142 = 180

= \(\frac{x}{2}\) + \(\frac{y}{2}\) = 38

= x + y = 76

In \(\Delta \)ABC,

\(\angle\)B + \(\angle\)C = 76

\(\angle\)A = 180 - 76

= \(\angle\)A = 104

Therefore, \(\angle\)A is \({104}^\circ\).