Question

ABCD is a cyclic quadrilateral ∠DBA=500 and ∠ADB = 330. Then the measure of ∠BCD is

Answer 1

Given:

ABCD is a cyclic quadrilateral ∠ DBA = 500 and ∠ ADB = 330.

To find:

Then the measure of ∠ BCD is

Solution:

Consider the attached figure while going through the following steps.

As given is a cyclic quadrilateral, we know that, the sum of opposite angles is 180°.

∴ ∠ DAB + ∠ BCD = 180°

Now consider, Δ ABD,

∠ ABD + ∠ BDA + ∠ DAB = 180°

⇒ 50° + 30° + ∠ DAB = 180°

⇒ 80° + ∠ DAB = 180°

⇒ ∠ DAB = 180° - 80°

∴ ∠ DAB = 100°

Let's consider, ∠ DAB + ∠ BCD = 180°

⇒ 100° + ∠ BCD = 180°

⇒ ∠ BCD = 180° - 100°

∴ ∠ BCD = 80°