If a diagonal of a rectangle is inclined to one side of the rectangle at 35 ∘ , then the acute angle between the diagonals is _____. Options: A . &nbsp 35 ∘ B . &nbsp 60 ∘ C . &nbsp 70 ∘ D . &nbsp 80 ∘

Answer: Option C : C Given: In rectangle ABCD, ∠ B A O = 35 ° To find: Angle between the diagonals ∠ A O D o r ∠ B O C In Δ AOB OA = OB ∵ Diagonals of a rectangle bisect each other ⇒ ∠ O B A = ∠ O A B = 35 ∘ (As the angles opposite to equal sides are equal) Applying exterior angle property in Δ AOB ∠ A O D = ∠ O B A + ∠ O A B ∠ A O D = 35 ° + 35 ° ∠ A O D = 70 °

If a diagonal of a rectangle is inclined to one side of the rectangle at 35∘,

Question

If a diagonal of a rectangle is inclined to one side of the rectangle at $35^{\circ}$ , then the acute angle between the diagonals is _____.

Options:

A .

35^{\circ}

B .

60^{\circ}

C .

70^{\circ}

D .

80^{\circ}

Answer: Option C
:
C

Given: In rectangle ABCD,
$∠ B A O = 35 °$
To find: Angle between the diagonals $∠ A O D o r ∠ B O C$
In $Δ$ AOB
OA = OB
$∵$ Diagonals of a rectangle bisect each other
$\Rightarrow ∠ O B A = ∠ O A B = 35^{\circ}$ (As the angles opposite to equal sides are equal)
Applying exterior angle property in $Δ$ AOB
$∠ A O D = ∠ O B A + ∠ O A B$
$∠ A O D = 35 ° + 35 °$
$∠ A O D = 70 °$