Question

The diagonals of a rectangle ABCD meet at O. If ∠𝐵𝑂𝐶 = ${44}^{\circ }$, find ∠𝑂𝐴𝐷.

• A. ${36}^{\circ }$
• B. ${48}^{\circ }$
• C. ${56}^{\circ }$
• D. ${68}^{\circ }$

Answer 1

The correct option is D ${68}^{\circ }$

ABCD is a rectangle and $\angle BOC={44}^{\circ }$[Given]

$\angle AOD=\angle BOC$
[Vertically opposite angles]

$\angle AOD=\angle BOC={44}^{\circ }$

$\angle OAD=\angle ODA$
[Since OD = OA, as length of diagonals in a rectangle are equal and diagonals bisect each other]

Since sum of the angles of a triangle is ${180}^{\circ }$, then

So, $\angle OAD=\frac{1}{2}\times ({180}^{\circ }-{44}^{\circ })={68}^{\circ }$