The angles formed by the side of the rhombus and its diagonals relate to each other as 7: 2.

The angles formed by the side of the rhombus and its diagonals relate to each other as 7: 2. Find the larger corner of the diamond.

Given: ABCD – rhombus, <BAO: <ABO = 7: 2; AC and BD are diagonals.

Find <A.

Solution.

1) Since ABCD is a rhombus, its diagonals are perpendicular, this is a property of the diagonals of a rhombus.

So triangle AOB is rectangular, angle BOA = 90.

2) Equality <BAO: <ABO = 7: 2 means that you can introduce the variable x.

Then <BAO = 7x, <ABO = 2x.

3) The sum of the angles of the triangle AOB is 180, which means 7x + 2x + 90 = 180; 9x = 90; x = 10.

<BAO = 7 * 10 = 70, then <A = 70 * 2 = 140.

Answer: 140.