The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O . If $∠ D A C = 35^{\circ} a n d ∠ A O B = 80^{\circ}$ , then $∠ D B C$ is equal to ___.

$55^{\circ}$

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$45^{\circ}$

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$75^{\circ}$

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$35^{\circ}$

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Solution

The correct option is B
$45^{\circ}$

Let $∠ D B C$ be 'x'

$∠ D A C = ∠ A C B = 35^{\circ}$ [Alternate angles]
Consider
$∠ A O B + ∠ B O C = 180^{\circ}$ [ Linear pair]
$∠ B O C = 180^{\circ} - 80^{\circ} = 100^{\circ}$
Consider $Δ B O C,$
$∠ B O C + ∠ O C B + ∠ C B O = 180^{\circ}$
$100^{\circ} + 35^{\circ} + x = 180^{\circ}$
$x = 180 - 135 = 45^{\circ}$
$∴ ∠ D B C i s 45^{\circ}$

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Similar questions

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. The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32° and ∠AOB = 70°, then ∠DBC = _______.

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O . If ∠ D A C = 35^{\circ} and ∠ A O B = 80^{\circ}, then find the value of ∠ D B C .

Q. The diagonals AC and BD of a parallelogram ABCD interest each other at the point O. If

∠ D A C = 30^{0}

and

∠ A O B = 72^{0}

, then find

∠ D B C

Q. Question 12
The diagonals AC and BD of a parallelogram ABCD intersect each other. The point O. If

∠ D A C = 32^{\circ} a n d ∠ A O B = 70^{\circ}, t h e n ∠ D B C

is equal to
(A)

24^{\circ}

(B)

86^{\circ}

(C)

38^{\circ}

(D)

32^{\circ}

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The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O . If ∠DAC=35∘ and ∠AOB=80∘, then ∠DBC is equal to ___.

The correct option is B 45∘ Let ∠DBC be 'x' ∠DAC=∠ACB=35∘ [Alternate angles] Consider ∠AOB+∠BOC=180∘ [ Linear pair] ∠BOC=180∘−80∘=100∘ Consider ΔBOC, ∠BOC+∠OCB+∠CBO=180∘ 100∘+35∘+x=180∘ x=180−135=45∘ ∴∠DBC is 45∘

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O . If $∠ D A C = 35^{\circ} a n d ∠ A O B = 80^{\circ}$ , then $∠ D B C$ is equal to ___.