ABCD is a parallelogram in which - DAC - 40- - - BAC - 30- - DOC - 105- - then - CDO equals -

The correct option is D 45^∘ ∠ AOB = ∠ COD = 105^∘ (Vertically Opposite Angles)In triangle AOB, ∠ BAO + ∠ AOB + ∠ OBA = 180^∘ 30^∘ + ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to Be Parallel

ABCD is a par...

Question

ABCD is a parallelogram in which $∠ D A C = 40^{\circ}; ∠ B A C = 30^{\circ}; ∠ D O C = 105^{\circ}$ ; then $∠ C D O$ equals :

75^{\circ}

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70^{\circ}

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40^{\circ}

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45^{\circ}

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Solution

The correct option is D $45^{\circ}$
$∠ A O B = ∠ C O D = 105^{\circ}$ (Vertically Opposite Angles)
In triangle $A O B,$
$∠ B A O + ∠ A O B + ∠ O B A = 180^{\circ}$
$30^{\circ} + 105^{\circ} + ∠ O B A = 180^{\circ}$
$∠ O B A = 45^{\circ}$

$A B$ and $C D$ are parallel
$∴ ∠ O B A = ∠ C D O = 45^{\circ}$ (Alternate Interior angles)

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Similar questions

ABCD is a cyclic quadrilateral in which :

(i) BC || AD, $A D C = 110^{o} a n d ∠ B A C = 50^{o}$ . Find $∠ D A C$ .

(ii) $∠ D B C = 80^{o} a n d ∠ B A C = 40^{o} .$ Find $∠ B C D$ .

(iii) $∠ B C D = 100^{o} a n d A B D = 70^{o}$ . Find $∠ A D B$ .

Q. The diagonals AC & BD of parallelogram ABCD intersect each other at P of

∠ D A C = 40^{o}

∠ A P B = 80^{o}

. Then

∠ D B C

is equal to ___ .

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O such that $∠ D A C = 30^{\circ} a n d ∠ A O B = 70^{\circ}$ . Then, $∠ D B C =$ ?

(a) $40^{\circ}$

(b) $35^{\circ}$

(d) $50^{\circ}$

Q. In the figure,

A B C D

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A C

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∠ D A C = 40^{\circ}, ∠ C A B = 35^{\circ}

; and

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ABCD is a parallelogram in which ∠DAC=40∘;∠BAC=30∘;∠DOC=105∘ ; then ∠CDO equals :

The correct option is D 45∘∠AOB=∠COD=105∘ (Vertically Opposite Angles)In triangle AOB,∠BAO+∠AOB+∠OBA=180∘30∘+105∘+∠OBA=180∘∠OBA=45∘AB and CD are parallel ∴∠OBA=∠CDO=45∘ (Alternate Interior angles)

ABCD is a parallelogram in which $∠ D A C = 40^{\circ}; ∠ B A C = 30^{\circ}; ∠ D O C = 105^{\circ}$ ; then $∠ C D O$ equals :