Consider Rectangle ABCD,
According to the problem, it is given that ∠OCD = 300.
We know that in a rectangle The sides are perpendicular to each other. So, we can write
⇒ ∠OCD + ∠OCB = 1800.
⇒ 300 + ∠OCB = 900
⇒ ∠OCB = 900 - 300
⇒ ∠OCB = 600.
We know that the alternate angles along the traversal line between two parallel lines are equal.
∠OCD = ∠OAB = 300.
∠OCB = ∠OAD = 600.
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 = 600.
From ΔOBC, we can say that,
∠O + ∠B + ∠C = 1800. (Sum of angles in a triangle is 1800)
By substituting the values we get,
⇒ ∠O + 600 + 600 = 1800.
⇒ ∠O + 1200 = 1800
⇒ ∠O = 1800 - 1200
⇒ ∠O = 600.
The value of ∠BOC is 600 and the ΔBOC is Equilateral Triangle.
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