The ratio of the angles formed by the side of the rhombus with its diagonals is 5: 4.

The ratio of the angles formed by the side of the rhombus with its diagonals is 5: 4. Find the obtuse angle of the rhombus.

The diagonals of the rhombus are the bisectors of the angles. This means that half of an obtuse angle refers to half of an acute angle as 5 to 4 (according to the conditions of the problem).

The sum of the obtuse and acute angles of a rhombus is 180 °, according to the rhombus property.

Let’s solve the problem using the equation, where:

5x – half an obtuse angle;

4x – half of an acute angle;

Means:

5x * 2 = 10x – obtuse angle of the rhombus;

4x * 2 = 8x – acute angle of the rhombus;

Let’s compose and solve the equation:

10x + 8x = 180 °;

18x = 180;

x = 180/18;

x = 10;

10x = 10 * 10 = 100 ° – obtuse angle of the rhombus.

Answer: 100 °