Prove the following: If, in a triangle \(ABC\), \(\angle BAO = \angle OAC = \angle 20^\circ \), \(\angle ACO= 10^\circ \) and \(\angle OCB = 30^\circ \), then \(\angle OBC = 80^\circ \). Try to use elementary geometry (Euclid's Elements).

Prove the following: If, in a triangle \(ABC\), \(\angle BAO = \angle OAC = \angle 20^\circ \), \(\angle ACO= 10^\circ \) and \(\angle OCB = 30^\circ \), then \(\angle OBC = 80^\circ \). Try to use elementary geometry (Euclid's Elements).

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