ABCD is a cyclic quadrilateral. Its …
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Gaurav Seth 3 years, 10 months ago
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.
(i) We know that the angles in the same segment are equal
So we get
∠BDC = ∠BAC = 40o
Consider △ BCD
Using the angle sum property
∠BCD + ∠BDC + ∠DBC = 180o
By substituting the values
∠BCD + 40o + 60o = 180o
On further calculation
∠BCD = 180o – 40o – 60o
By subtraction
∠BCD = 180o – 100o
So we get
∠BCD = 80o
(ii) We know that the angles in the same segment are equal
So we get
∠CAD = ∠CBD
So ∠CAD = 60o
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