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ABCD is a cyclic quadrilateral. Its …

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ABCD is a cyclic quadrilateral. Its diagonals intersect at point P. Angle BAC is 40 degree. Angle DBC is 80 degree find angle BCD.

Posted by Janani Surya 5 years, 1 month ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month 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 = 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

0Thank You

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