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. 35°
• B. 60°
• C. 70°
• D. 80°

Answer 1

The correct option is C

70°

The angle to be found is the acute angle between diagonals BD and AC. That is, ∠AOD or ∠BOC.

Since diagonals of a rectangle are equal, we know that AO = OB.

Hence, ∠OBA = ∠OAB = ${35}^{\circ }$

So, ∠AOB = ${180}^{\circ }-{35}^{\circ }-{35}^{\circ }={110}^{\circ }$ (By angle sum property of a triangle)

Thus, ∠AOD = ${180}^{\circ }-{110}^{\circ }={70}^{\circ }$ (Angles on a straight line are supplementary)