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Question:

In the figure (not drawn to scale) given below, if AD = CD = BC, and ∠BCE = 96°, how much is ∠DBC?

Explanation:

∵ AD = DC,

∴ ∠DAC = ∠DCA = x

∴ ∠CDB = ∠DAC + ∠DCA = 2x

∵ DC = BC

∴ ∠CDB = ∠CBD = 2x

Also,

x + y = 180° − 96° = 84°               ... (i)

y + 4x = 180°                                 ... (ii)

Solving (i) and (ii), we get,

x = 32°

∴ ∠DBC = 2x = 64°

Hence, option (c).