Find the angles of a rhombus if the ratio of the angles that the diagonals form with a side is 6:9.

Answer 1

When you draw out a rhombus with two diagonals you create four right triangles with the center angle being 90 degrees. If it's a right triangle then the angles opposite the right angle are complimentary. In the question given you are told the ratio of those angles are 6:9 (or 2:3). Therefore the sum of the ratios with the unknown constant will be 90 (2x + 3x = 90). After combining like terms and dividing by the coefficient x = 18. Then applying that constant to the ratios (2 x 18 and 3 x 18) then the angles are 36 and 54 degrees.