In a ΔABC, the bisectors of ∠B and ∠C meet at O. If ∠BOC = 142°, then the measure of ∠A is:
Answer & explanation
Correct answer: option 3
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 \({104}^\circ\).