1.

In the given figure if AD = DC = BC and ∠BCE=96∘ then ∠DBC is

Answer»

Given:- AD = CD = BC

Sol:- Since,  AD = CD = BC so, 

∠CAD = DCA and ∠CDB =  ∠DBC

Let ∠CAD be x° and ∠CDB be y°

In ∆CAD, by exterior angle property

y = 2x ∴ x = y/2 -- (1)

In ∆CAB, by exterior angle property, 

x + y = 96° 

 y/2 + y = 96° (From 1) 

 3y/2 = 96°

∴ y = 32 × 2 = 64° 

Therefore, ∠DBC is 64°



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