Question

In order for the parallelogram to be a rhombus x=? Given 2x-15 of one side angle and 3x of the other

Answer 1

x`~~ 207.8873386^o` if 2x-15 and 3x are calculated in radiant;
`x = 39^o` if 2x-15 and 3x are calculated in degrees.

Explanation:

expecting both 2x-15 and 3x are angles in radiant
let's draw a rhombus ABCD
`angle`ABC = 2x-15
`angle`BCD = 3x
`because` AB//CD
`therefore` `angle`ABC + `angle`BCD = `pi` (`180^o` in radiant)

2x - 15 + 3x = `pi`
5x - 15 = `pi`
x - 3 = `1/5pi`
x = `1/5pi + 3 ~~ 3.628318531 ~~ 207.8873386^o`

now expecting both 2x-15 and 3x are angles in degrees
`2x -15^o + 3x = 180^o`
`5x - 15^o = 180^o`
`5x = 195^o`
`x = 39^o`

Answer 2

For a parallelogram to be equal, the lengths of all the sides have to be the same. Having lines parallel does not make them equal.

Opposite angles of both rhombuses and parallelograms are equal and co-interior angles of both sum to `180°`, but the size of the angles is not affected by the lengths of the sides between them.