In the figure (not drawn to scale) given below, if AD =

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In the figure (not drawn to scale) given below, if AD = DC = BC and ∠BCE = 96°, then ∠DBC is :

1. 32°
2. 84°
3. 64°
4. 96°

Correct Option: C

From given figure ,

Let ∠ACD = a = ∠DAC
∴ ∠CDB = 2a = ∠CBD
The angles of the base of an isosceles triangle are equal.
∴ ∠ACB = 180° – 96° = 84°
⇒ ∠ACD + ∠DCB = 84°
⇒ a + 180° – 4a = 84°
⇒ 180° – 3a = 84°
⇒ 3a = 180° – 84° = 96°
⇒ a = 96 ÷ 3 = 32°
⇒ ∠DBC = 2a = 64°