In rectangular ABCD, diagonal lines AC and BD intersect at point O, AE bisects ∠ bad, AE intersects BC at point E. if ∠ CAE = 15 °, what is the degree of ∠ BOE?
∵ the quadrilateral ABCD is a rectangle
∴∠DAB=∠ABC=90°
∵ AE bisection ∠ bad
∴∠DAE=∠EAB=45°
ABC = 90 degree
The Abe is an isosceles right triangle
∴AB=BE
∵∠OAE=15°
∴∠DAC=30°=∠DBC
The easy syndrome △ OAB is an equilateral triangle
∴AO=BO=AB=BE
∴∠BOE=∠OEB=(180°—30°)÷2=75°
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