The diagonals AC and BD of a -parallelogram nbsp- ABCD intersect each other -at the point O - If - DAC -35- and - AOB-80- then find the value of - DBC- nbsp-45-75-35-55-

The correct option is A 45^∘Let ∠ DBC be x. AD ∥ CB and AC acts as the transversal. ∠ DAC =∠ ACB =35^∘ (∵Alternate interior angles are equal) In BOC ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Properties of Parallelogram

The diagonals...

Question

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

55^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

45^{\circ}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

75^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

35^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $45^{\circ}$
$Let ∠ D B C be x$ .

$A D ∥ C B and A C acts as the transversal. ∠ D A C = ∠ A C B = 35^{\circ} (∵ Alternate interior angles are equal)$

$In △ B O C, by exterior angle property ∠ B C O + ∠ O B C = 80^{\circ} 35^{\circ} + x = 80^{\circ} x = 80^{\circ} - 35^{\circ} x = 45^{\circ}$

Suggest Corrections

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) $50^{\circ}$

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 .

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 ___.

Calculate the mode of the following data:

Class-interval	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$	$75 - 85$
Frequency	$5$	$4$	$7$	$12$	$8$	$1$	$4$

Class intervals / Frequency

15-25. 6

25-35. 11

35-45 . 7

45-55. 4

55-65. 4

65-75. 2

75-85 . 1

Join BYJU'S Learning Program

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

The correct option is B 45∘Let ∠DBC be x. AD∥CB and AC acts as the transversal. ∠DAC=∠ACB=35∘(∵Alternate interior angles are equal) In △BOC, by exterior angle property∠BCO+∠OBC=80∘35∘+x=80∘x=80∘−35∘x=45∘

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