Answer :

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.


So,


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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