Question

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

Answer 1

This is answer ...Hope it helps you

Answer 2

Heya....

Here is your answer....

ABCD is a cyclic quadrilateral whose diagonal intersect at E.

∠CBD = ∠CAD (Angles in 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°

In ΔABC,

AB = BC (Given)

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

⇒ ∠BCA = 30°

But ∠BCD = 80°.

⇒ ∠BCA + ∠ACD = 80°

30° + ∠ACD = 80°

⇒ ∠ACD = 50°

⇒ ∠ECD = 50°.

Thanks...!!!

XD

Sorry baby 'wink'