. Diagonal AC of the rhombus ABCD is equal to side AD. Find all the an

1.	. Diagonal AC of the rhombus ABCD is equal to side AD. Find all the angles of the rhombus.
Answer» In a Rhombus the diagonals are perpendicular to each other meeting at the center O. In the triangle BOC, ∠O = 90°. Sin ∠OBC = OC / BC = (1/2 AC) / BC = 1/2 so ∠OBC = 30° so angle∠ABC = 2 * 30° =60° Then ∠OCB-∠OBC = 60° so ∠DCB = 2 * 60° =120° The angles of Rhombus are 60 and 120 deg.

. Diagonal AC of the rhombus ABCD is equal to side AD. Find all the angles of the rhombus.

Answer»

In a Rhombus the diagonals are perpendicular to each other meeting at the center O.

In the triangle BOC, ∠O = 90°. Sin ∠OBC = OC / BC = (1/2 AC) / BC = 1/2 so ∠OBC = 30° so angle∠ABC = 2 * 30° =60°

Then ∠OCB-∠OBC = 60° so ∠DCB = 2 * 60° =120°

The angles of Rhombus are 60 and 120 deg.