1.

In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC =(a) 60o (b) 30o (c) 150o (d) 120o

Answer»

(a) 60o

From the given figure,

∠BAD = 30o

∠BCD = 30o … [∵opposite angles of parallelogram are equal]

Now, let us consider the triangle CBD

From angle sum property, ∠DBC + ∠BCD + ∠CDB = 180o

90o + 30o + ∠CDB = 180o

120o + ∠CDB = 180o

∠CDB = 180o – 120o

∠CDB = 60o

∴∠BEC = 60o, because opposite angles of parallelogram are equal.



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