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).
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