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

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Solution

Given:
The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O
∠DAC = 32°
∠AOB = 70°

Let ∠DBC be x.

Since, AB || DC
Therefore, ∠DAC = ∠ACB = 32° (alternate angles)

Also, ∠AOB + ∠BOC = 180° (angles on a straight line)
⇒ 70° + ∠BOC = 180°
⇒ ∠BOC = 180° − 70°
⇒ ∠BOC = 110°

In ∆COB,
∠OCB + ∠CBO + ∠BOC = 180°
⇒ 32° + x + 110° = 180°
⇒ x + 142° = 180°
⇒ x = 180° − 142°
⇒ x = 38°

Hence, ∠DBC = 38°.

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Similar questions

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If $∠$ DAC = $32^{\circ}$ and $∠$ AOB = $70^{\circ}$ , then ∠DBC is equal to:

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

∠ D A C = 32^{\circ}, ∠ A O B = 70^{\circ},

then

∠ D B C

is equal to :

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

If ∠DAC = 32° and ∠AOB = 70°, then find the measure of ∠DBC.

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}

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) $50^{\circ}$

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