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The Diagonals AC and BD of a Parallelogram ABCD intersect each other at the point O such that ∠DAC = 30∘ and ∠AOB = 70∘. Then, ∠DBC?
- a)30∘
- b)45∘
- c)35∘
- d)40∘
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The Diagonals AC and BD of a Parallelogram ABCD intersect each other a...
∠ OAD = ∠ OCB = 30∘
(Alternate interior angles)
∠ AOB + ∠ BOC = 180∘
(Linear pair of angles)
∴ ∠ BOC =180∘ − 70∘ = 110∘
(∠ AOB = 70∘)
In ∆ BOC, we have:
∠ OBC = 180∘ − (110∘ + 30∘) = 40∘
∴ ∠ DBC = 40∘
(Alternate interior angles)
∠ AOB + ∠ BOC = 180∘
(Linear pair of angles)
∴ ∠ BOC =180∘ − 70∘ = 110∘
(∠ AOB = 70∘)
In ∆ BOC, we have:
∠ OBC = 180∘ − (110∘ + 30∘) = 40∘
∴ ∠ DBC = 40∘
Most Upvoted Answer
The Diagonals AC and BD of a Parallelogram ABCD intersect each other a...
AO = 5, OC = 7, and OD = 9. Find the length of OB.
We know that in a parallelogram, opposite sides are equal in length, so AB = CD and BC = AD. Let x be the length of OB.
By the properties of diagonals in parallelograms, we know that AO/OC = BO/OD. Substituting the given values, we have:
5/7 = x/9
Solving for x, we get:
x = 9(5/7) = 6.43 (rounded to two decimal places)
Therefore, the length of OB is approximately 6.43 units.
We know that in a parallelogram, opposite sides are equal in length, so AB = CD and BC = AD. Let x be the length of OB.
By the properties of diagonals in parallelograms, we know that AO/OC = BO/OD. Substituting the given values, we have:
5/7 = x/9
Solving for x, we get:
x = 9(5/7) = 6.43 (rounded to two decimal places)
Therefore, the length of OB is approximately 6.43 units.
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