Question

In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = ______.

Options

• 60°

• 30°

• 150°

• 120°

Answer 1

In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = 60°.

Explanation:

Given: ∠BAD = 30°

So, ∠BCD = 30°   ...[Opposite angles of a parallelogram are equal]

Now, In triangle CBD: 

∠DBC + ∠BCD + ∠CDB = 180°   ...[Sum of all angles of a triangle is equal to 180°]

90° + 30° + ∠CDB = 180°

∠CDB = 180° – 90° – 30°

∠CDB = 180° – 120°

∠CDB = 60°

Therefore, ∠BEC = 60°  ...[Opposite angles of a parallelogram are equal]