ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $∠ D B C = 80^{\circ}$ and $∠ B A C = 40^{\circ},$ then find $∠ B C D$ .

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Solution

Given that $∠ B A C = 40^{\circ} and ∠ D B C = 80^{\circ} .$

Since the angles formed by the same segment are equal,
$∠ B D C = ∠ B A C = 40^{\circ} .$

$In Δ B D C,$

$∠ B D C + ∠ D B C + ∠ B C D = 180^{\circ} . [Angle sum property]$

i.e., $40^{\circ} + 80^{\circ} + ∠ B C D = 180^{\circ}$

$⟹ ∠ B C D = 180^{\circ} - 120^{\circ} = 60^{\circ}$

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Similar questions

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $∠ D B C = 80^{\circ}$ and $∠ B A C = 40^{\circ},$ then find $∠ B C D$ .

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40^{\circ},

find

∠ B C D

in degrees.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $∠ D B C = 80^{\circ}$ and $∠ B A C = 40^{\circ},$ then find $∠ B C D$ .

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $∠ D B C = 70^{\circ}$ and $∠ B A C = 30^{\circ}$ , then find $∠ B C D$ . Further, if AB = BC, then find $∠ E C D$ .

A B C D

is a cyclic quadrilateral whose diagonals intersect at a point

E

. If

∠ D B C = 70^{o}, ∠ B A C = 30^{o}

, find

∠ B C D

. Further, if AB= BC, find

∠ E C D

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ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=80∘ and ∠BAC=40∘, then find ∠BCD.

Given that ∠BAC=40∘ and ∠DBC=80∘. Since the angles formed by the same segment are equal, ∠BDC=∠BAC=40∘. In ΔBDC, ∠BDC+∠DBC+∠BCD=180∘. [Angle sum property] i.e., 40∘+80∘+∠BCD=180∘ ⟹∠BCD=180∘−120∘=60∘

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $∠ D B C = 80^{\circ}$ and $∠ B A C = 40^{\circ},$ then find $∠ B C D$ .