Question

A diagonal of a rectangle is inclined to one side of the rectangle at 35°. The acute angle between the diagonals is
(a) 55°
(b) 70°
(c) 45°
(d) 50°

Answer 1

Given: In rectangle ABCD, ∠OAD = 35°.

Since, ∠BAD = 90°

$\Rightarrow$ ∠OAB = 90° $-$ 35° = 55°

In ΔOAB,

Since, OA = OB (Diagonals of a rectangle are equal and bisect each other)

$\Rightarrow$ ∠OAB = ∠OBA = 55° (Angles opposite to equal sides are equal)

Now, in ΔODA,

55° + 55° + ∠DOA = 180° (Angle sum property of a triangle)

$\Rightarrow$ ∠DOA = 180° $-$ 110°

$\Rightarrow$ ∠DOA = 70°

Thus, the acute angle between the diagonals is 70°.

Hence, the correct option is (b).