Question
ABCD is a cyclic quadrilateral and BC is a diameter of
the circle. If ∠DBC = 29°, then ∠BAD = ?Solution
According to the question ∠DBC = 29° ∠BDC = 90° [Angle in a semicircle is 90°] We know that sum of all the sides of triangles is 180° ⇒ ∠DBC + ∠BDC + ∠BCD = 180° ⇒ 29° + 90° + ∠BCD = 180° ⇒ 119° + ∠BCD = 180° ⇒ ∠BCD = (180° – 119°) ⇒ ∠BCD = 61° Now, We know that, the opposite angles in a cyclic quadrilateral is 180° So, ⇒ ∠BAD + ∠BCD = 180° ⇒ ∠BAD + 61° = 180° ⇒ ∠BAD = (180° – 61°) ⇒ ∠BAD = 119°
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