IntheacutetriangleABC(图7.6-4),ADisperpendiculartoBC,andCEisperpendiculartoAB,if∠AOE=58°,then∠BAC+∠BCA=.

Question

In the acute triangle ABC(图7.6-4),AD is perpendicular to BC,and CE is perpendicular to AB,if
∠AOE=58°,then ∠BAC+∠BCA=_________.

Answer 1

1.∠BAC +∠ACE=90°
2.∠BCA + ∠CAD=90°
1+2 =∠BAC+∠BCA+∠ACE+∠CAD=180°
∠ACE+∠CAD=∠AOE=58°
=>∠BAC+∠BCA=180°-58°=122°