BHC=∠EHD。
From the intersection of heights BD and CE at point H, we get
∠ADH=∠AEH=90。
From the theorem of sum of internal angles of quadrilateral
∠A+∠AEH+∠EHD+∠HDA=360,
∠A+∠EHD = 360-∠AEH-∠HDA = 360-90-90 = 180,
∴∠bhc+∠a= 180;
(2) Because ∠BHC and ∠EHD are diagonal, we get
BHC=∠EHD。
From the intersection of heights BD and CE at point H, we get
∠ADH=∠AEH=90。
From the theorem of sum of internal angles of quadrilateral
∠H+∠AEH+∠EHD+∠HDA=360,
∠H+∠DAE = 360-∠AEH-∠HDA = 360-90-90 = 180,
∴∠BHC+∠BAC= 180。