In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that

Question:

In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that DBC = 60° and ∠BAC = 40°. Find

(i) ∠BCD,

(ii) ∠CAD.

 

Solution:

(i) ∠BDC = ∠BAC = 40°  (Angles in the same segment)
In 
ΔBCD, we have:
 ∠BCD + ∠DBC + ∠BDC = 180°  (Angle sum property of a triangle)        
⇒ ∠BCD + 60° + 40° = 180°
⇒ ∠BCD = (180° - 100°) = 80°

(ii) ∠CAD = ∠CBD  (Angles in the same segment)
= 60°

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