In the given figure, ∠ABC = 81° and ∠ACB = 9°. What is the value of ∠BDC?

80° 90° 70° 60°

90°

⇒ In \(\Delta \)ABC ⇒ ∠ABC + ∠ACB + ∠BAC = 180°  (Angle sum property) ⇒ 81° + 9° + ∠BAC = 180° ⇒ ∠BAC = 180° - 90° = 90° Now, ⇒ ∠BAC  = ∠BDC = 90° (angle in same segment) Therefore, the answer is ∠BDC = 90°.