As shown in the figure, in rectangular ABCD, the bisector of ∠ bad intersects BC at point E, and point O is the intersection of diagonals, and ∠ CAE = 15 °, then ∠ BOE=______ Degree

As shown in the figure, in rectangular ABCD, the bisector of ∠ bad intersects BC at point E, and point O is the intersection of diagonals, and ∠ CAE = 15 °, then ∠ BOE=______ Degree

As shown in the figure, connecting OE; ∵ quadrilateral ABCD is a rectangle, and EA bisects ∵ bad, ∵ BAE = 45 °; ∵ Abe is an isosceles right triangle, ab = be; ∵ CAE = 15 °, ∵ Bao = ∵ CAE + ∵ BAE = 60 °; and ∵ OA = ob, ∵ △ Bao is an equilateral triangle, ab = Bo; ∵ Bo = be; ∵ OBC = 90 ° - ∵ ABO = 30 °; ∵ BOE = (180 ° - 30 °) △ 2 = 75 °. So the answer is 75