Question

In the given below figure,
∠ BAD = 65°
∠ ABD = 70°
∠ BDC = 45°
Find: (i) ∠ BCD,  (ii) ∠ ADB.
Hence show that AC is a diameter.

Answer 1

Given:
∠ BAD = 65°
∠ ABD = 70°
∠ BDC = 45°

(i) Quadrilateral ABCD is cyclic quadrilateral.
∴ ∠ DAB + ∠ BCD = 180°
∴ 65° + ∠ BCD = 180°
∴ ∠ BCD = 180° - 65°
∴ ∠ BCD = 115°

(ii) In ΔADB,
∴ ∠ DAB + ∠ ABD + ∠ ADB = 180°
∴ 65° + 70° + ∠ ADB = 180°
∴ ∠ ADB = 180° - 135°
∴ ∠ ADB = 45°.