Answer :

Consider Rectangle **ABCD**,

According to the problem, it is given that **∠****OCD = 30 ^{0}**.

We know that in a rectangle The sides are perpendicular to each other. So, we can write

⇒ **∠****OCD +** **∠****OCB = 180 ^{0}**.

⇒ 30^{0} + ∠OCB = 90^{0}

⇒ ∠OCB = 90^{0} - 30^{0}

⇒ **∠****OCB = 60 ^{0}**.

We know that the alternate angles along the traversal line between two parallel lines are equal.

So,

**∠****OCD =** **∠****OAB = 30 ^{0}**.

**∠****OCB =** **∠****OAD = 60 ^{0}**.

We know that the diagonals in a rectangle bisect each other.

So, we can say that,

**AO = OB = OC = DO**.

We also the angles opposite to the equal sides are also equal.

So, From the figure, we can say that

**∠****OBC =** **∠****OCB = 60 ^{0}**.

From **ΔOBC**, we can say that,

**∠****O +** **∠****B +** **∠****C = 180 ^{0}**. (Sum of angles in a triangle is 180

^{0})

By substituting the values we get,

⇒ ∠O + 60^{0} + 60^{0} = 180^{0}.

⇒ ∠O + 120^{0} = 180^{0}

⇒ ∠O = 180^{0} - 120^{0}

⇒ **∠****O = 60 ^{0}**.

The value of **∠****BOC** is **60 ^{0}** and the

**ΔBOC**is

**Equilateral Triangle**.

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