In the adjacent rectangle ABCD, ∠OCD = 30°. Calculate ∠BOC. What type of triangle is BOC?

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.