The diagonals of the rectangle intersect at an angle of 20 degrees. Find the corners that form a diagonal

The diagonals of the rectangle intersect at an angle of 20 degrees. Find the corners that form a diagonal with the sides of the rectangle.

Given: ABCD is a rectangle, AC and BD are the diagonals of the rectangle, O is the point of intersection of the diagonals, ∠ BOA = 20.

Find: ∠ ОВА, ∠ ОВС -?

Decision:

According to the property of the diagonals of the rectangle, Δ AOB = Δ COD, and Δ BOC = Δ AOD.

Therefore, ∠ ОВА = ∠ ОАВ = ∠ OCD = ∠ОDC = (180 – 20) / 2 = 80.

∠ ВOС = ∠ AOD = 180 – 20 = 160.

∠ СВO = ∠ BCO = ∠ DAO = ∠ ADO = (180 – 160) / 2 = 10.

Answer: ∠ ОВА = 80, ∠ ОВС = 10.