Question

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If angle DBC = 70°,
angle BAC is 30°, find BCD. Further, if AB=BC, find ECD.​

Answer 1

Answer:

50°

Step-by-step explanation:

For chord CD,

∠CBD = ∠CAD (Angles on the same segment are equal)

∠CAD = 70°

∠BAD = ∠BAC + ∠CAD

= 30° + 70°

= 100°

∠BCD + ∠BAD = 180° (Opposite angles of a cyclic quadrilateral)

∠BCD + 100° = 180°

∠BCD = 80°

Now, In ΔABC,

AB = BC (Given)

∠BCA = ∠CAB (Angles opposite to equal sides of a triangle)

∠BCA = 30°

We have,

∠BCD = 80°

∠BCA + ∠ACD = 80°

30° + ∠ACD = 80°

∠ACD = 50°

As ∠ACD = ∠ECD