In the given figure, ABCD is a cyclic quadrilateral whose diagonals in

1.	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.
Answer» (i) We know that the angles in the same segment are equal So we get ∠BDC = ∠BAC = 40^o Consider △ BCD Using the angle sum property ∠BCD + ∠BDC + ∠DBC = 180^o By substituting the values ∠BCD + 40^o + 60^o = 180^o On further calculation ∠BCD = 180^o – 40^o – 60^o By subtraction ∠BCD = 180^o – 100^o So we get ∠BCD = 80^o (ii) We know that the angles in the same segment are equal So we get ∠CAD = ∠CBD So ∠CAD = 60^o

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.

Answer»

(i) We know that the angles in the same segment are equal

So we get

∠BDC = ∠BAC = 40^o

Consider △ BCD

Using the angle sum property

∠BCD + ∠BDC + ∠DBC = 180^o

By substituting the values

∠BCD + 40^o + 60^o = 180^o

On further calculation

∠BCD = 180^o – 40^o – 60^o

By subtraction

∠BCD = 180^o – 100^o

So we get

∠BCD = 80^o

(ii) We know that the angles in the same segment are equal

So we get

∠CAD = ∠CBD

So ∠CAD = 60^o

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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.

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