Find the angles of the rhombus if the ratio of the angles formed by the diagonals and the sides is 4:5.

Answer 1

if the ratio of those angles are 4:5, the ratio of the angles of the rhombus are also 4:5. The sum of adjacent angles of a rhombus is 180. 4x+5x=180, 9x=180, x=20, so the angles are 80, 100, 80, and 100

Answer 2

call one of the angles 4x and the other one 5 x
the total angle in the 4x corner is 8x (diagonal crossing parallel lines, 4x + 4x = 8x)
the total angle in the 5x corner is 10 x
the sum if all 4 corners is 16 x + 20 x = 36 x
36 x - 360
x = 10
8x = 80 degrees
10 x = 100 degrees