Choose the correct answer from the alternatives given :
ABCD is a cyclic quadrilateral. Diagonals AC and BD meets at P. If $∠ A P B$ = $110^{\circ}$ and $∠ C B D$ = $30^{\circ}$ , then $∠ A D B$ measures

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Solution

The correct option is C 80 $^{\circ}$

$∠$ ABD = ?
$∠$ CBD = $∠$ CAD = $30^{\circ}$
$∠$ DPA = $70^{\circ}$
In $Δ$ DPA,
$∠$ ADP + $∠$ DPA + $∠$ PAD = $180^{\circ}$
$∠$ ADP + $70^{\circ} + 30^{\circ} = 180^{\circ}$
$∠$ ADP = $80^{\circ}$
$∠$ ADP = $∠$ ADB = $80^{\circ}$

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Similar questions

Q. In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If

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and

∠ B A C = 45^{\circ}

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= ___ .

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 $∠ B C D$ = ___.

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

In cyclic quadrilateral ABCD

AD =BC,

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(i) $∠ B C D$ (ii) $∠ B C A$

(iii) $∠ A B C$ (iv) $∠ A D C$

Q. ABCD is a cyclic quadrilateral such that ∠ADB = 30° and ∠DCA = 80°, then ∠DAB =

(a) 70°

(b) 100°

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Choose the correct answer from the alternatives given :ABCD is a cyclic quadrilateral. Diagonals AC and BD meets at P. If ∠APB = 110∘ and ∠CBD = 30∘ , then ∠ADB measures

The correct option is C 80∘∠ABD = ?∠ CBD = ∠CAD = 30∘∠ DPA = 70∘In Δ DPA,∠ADP + ∠DPA + ∠PAD = 180∘∠ADP + 70∘+30∘=180∘∠ADP = 80∘∠ADP = ∠ADB = 80∘

Choose the correct answer from the alternatives given :
ABCD is a cyclic quadrilateral. Diagonals AC and BD meets at P. If $∠ A P B$ = $110^{\circ}$ and $∠ C B D$ = $30^{\circ}$ , then $∠ A D B$ measures

The correct option is C 80 $^{\circ}$

$∠$ ABD = ?
$∠$ CBD = $∠$ CAD = $30^{\circ}$
$∠$ DPA = $70^{\circ}$
In $Δ$ DPA,
$∠$ ADP + $∠$ DPA + $∠$ PAD = $180^{\circ}$
$∠$ ADP + $70^{\circ} + 30^{\circ} = 180^{\circ}$
$∠$ ADP = $80^{\circ}$
$∠$ ADP = $∠$ ADB = $80^{\circ}$