Question

Prove the 6 question number with diagram

Answer 1

Hi,  Chinmaykalita very good morning to u i hope this will help u

ABCD is a cyclic quadrilateral   (Given)   [ figure attached]

Diagonal intersects at E.   (Given)

∠BAC = 30° and ∠DBC = 70°   (Given)

RTP:-

1]∠BCD.

2]if AB=BC find ∠ECD.  

Proof:-

∠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°  .....................ANS [1]

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°.........................ANS[2]