Question

In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. if angle DBC = 45° and angle BAC = 55°, find angle BCD​

Answer 1

Answer:

BCD = 80

Step-by-step explanation:

BAC=BDC=55 (Lie on same segment)... 1

In triangle BCD, We have

BCD+DBC+BDC=180 ( sum of angle of triangle)

BCD+45+55= 180 (using 1 above)

BCD+100 = 180

BCD = 180-100

BCD = 80

Hence, angle BCD =80

Answer 2

Given:

• ∠DBC = 45°
• ∠BAC = 55°

To find:

⟶  ∠BCD = ?

Method:

In Major segment DABC,

We know that angles in the same segment are equal.

So ∠CAD = ∠CBD = 45°

Now,

∠BAD = ∠BAC + ∠CAD

⇒ ∠BAD = 55° + 45°

∴ ∠BAD = 100°

In Cyclic Quadrilateral ABCD,

Sum of opposite angles in a cyclic quadrilateral is 180°

⇒ ∠BAD + ∠BCD = 180°

⇒ 100° + ∠BCD = 180°

⇒ ∠BCD = 180° - 100°

∴ ∠BCD = 80°