If O is the orthocentre of a ΔABC and ∠BOC=140
∘
, then the measure of ∠BAC is:

In any triangle where O is the orthocentre (the intersection point of altitudes), the relationship between the angle formed at the orthocentre and the opposite vertex angle is given by:
∠BOC+∠BAC=180
∘

Given ∠BOC=140
∘
:

140
∘
+∠BAC=180
∘

∠BAC=180
∘
−140
∘
=40
∘