Question

A diagonal of a rectangle is inclined to one side of the rectangle at ${35}^{\circ }$. The acute angle between the diagonals is

(a) ${55}^{\circ }$

(b) ${70}^{\circ }$

(c) ${45}^{\circ }$

(d) ${50}^{\circ }$

Answer 1

ANSWER:
Given: In rectangle ABCD, ∠OAD = 35°.
Since, ∠ BAD = 90°
⇒ ∠OAB = 90° - 35° = 55°
In Δ OAB,
Since, OA = OB
(Diagonals of a rectangle are equal and bisect each other)
⇒ ∠OAB = ∠OBA = 55°
(Angles opposite to equal sides are equal)
Now, in ΔODA,
55° + 55° + ∠DOA = 180°
(Angle sum property of a triangle)
⇒ ∠DOA = 180° - 110°
⇒ ∠DOA = 70°
Thus, the acute angle between the diagonals is 70°.
Hence, the correct option is (b).