Question

1. In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If 2 DBC = 55° and Z BAC = 45°, find 2 BCD. A B​

Answer 1

Given:

ABCD is a cyclic quadrilateral

AC and BD are its diagonals

∠DBC = 55° and ∠BAC = 45°

To Find:

∠BCD

Solution:

The angle in the figure of the same arc are equal.

Therefore, ∠DBC = ∠DAC

⇒∠DAC = 55°

Now, ∠DAB = ∠DAC + ∠CAB

⇒∠DAB = 55° + 45° = 100°

⇒∠DAB = 100°

We know that the sum of opposite angles of a cyclic quadrilateral is always equal to 180°

∴ ∠BCD + ∠DAB = 180°

⇒ ∠BCD = 180° - ∠DAB

⇒ ∠BCD = 180°-100°

⇒ ∠BCD = 80°

∴ The measure of ∠BCD = 80°.