Quadrangle ABCD is inscribed in a circle. The angle ABC is 92 °, the angle CAD is 60 °. Find the angle ABD.

∠CAD is an inscribed angle and relies on the CD arc.
∠CBD is also inscribed and also relies on the same arc of the CD, therefore:
∠CAD = ∠CBD = 60 °
∠ABD = ∠ABC-∠CBD = 92 ° -60 ° = 32 °
Answer: 32

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