ABCD is a rectangle such that, diagonal AC and BD bisect at O. If ∠DCA = 60°, then what is ∠AOB?

Option 4 : 60°

**Given:**

ABCD is a rectangle

∠DCA = 60°

**Concept used:**

Diagonal of a rectangle are equal and bisect each other.

Opposite sides are parallel to each other.

Angle sum property

**Calculation:**

In rectangle ABCD,

AB ∥ CD

∠DCA = 60°

⇒ ∠DCA = ∠OAB [Alternate interior angle]

⇒ ∠OAB = 60°

In triangle AOB,

OA = OB [Diagonals are equal and bisect each other]

⇒ ∠OAB = ∠OBA [Angle opposite to equal sides are equal]

⇒ ∠OAB = ∠OBA = 60°

By using the angle sum property,

∠OAB + ∠OBA + ∠AOB = 180°

⇒ 60° + 60° + ∠AOB = 180°

⇒ ∠AOB = 60°

**∴ ∠AOB = 60°.**