H is the orthocentre of an acute-angled triangle ABC in which ∠BAC = 70°. What is the measure of ∠BHC?

Let the altitude from B meet AC at E and the altitude from C meet AB at F. In quadrilateral AFHE the angles at F and E are 90° each, so ∠FHE = 360° − 90° − 90° − 70° = 110°. ∠BHC is vertically opposite ∠FHE, so ∠BHC = 110°, matching the standard result ∠BHC = 180° − A. The traps come from mixing up the centres: 140° is $2A$, which is ∠BOC at the CIRCUMCENTRE, and 125° is 90° + A/2, which is ∠BIC at the INCENTRE.