In a cyclic quadrilateral ABCD, AB is the diameter of the circle. If ∠ACD is 40°, what is the measure of ∠BAD?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 50°.
If AB is the diameter, then ∠ACB = 90° (Angle subtended by the diameter at the circumference)
∠BCD = ∠BCA + ∠ACD = 90° + 40° = 130°
Opposite angles of a cyclic quadrilateral sum to 180°.
∠BAD + ∠BCD = 180°
⇒ ∠BAD + 130° = 180°
⇒ ∠BAD = 180° - 130° = 50°