Question

若o是三角形abc的外心,角boc=140度,求角a的度数

Answer 1

因为O是三角形ABC的外心

所以OA = OB = OC

所以∠OAC = ∠OCA,∠OAB = ∠OBA ,∠OBC = ∠OCB

因为∠BOC = 140°

所以 ∠OBC = ∠OCB = 20°

又因为 ∠OAC + ∠OCA + ∠OAB + ∠OBA + ∠OBC + ∠OCB = 180°

所以∠OAC + ∠OCA + ∠OAB + ∠OBA = 140°

所以 2∠OAB + 2∠OAC = 140°

所以 ∠OAB + ∠OAC = 70°

所以 ∠A = 70°