A rhombus has an area of 40 cm^2 and adjacent angles of 50° and 130° Find the length of a side of the rhombus.​

Please look down below

Step-by-step explanation:

∠1 + 69 + 47 = 180 (because straight line)

∠1 = 180 - 116

∠1 = 64

∠2 + ∠1 + 63 = 180 (because triangle)

∠2 + 64 + 63 = 180

∠2 = 180 - 127

∠2 = 53

∠3 + ∠1 = 180 (because straight line)

∠3 + 64 = 180

∠3 = 116

∠5 = ∠4 (given)

∠5 + ∠4 + ∠3 = 180

Denote ∠5 and ∠4 as x, so 2x

2x + ∠3 = 180

2x + 116 = 180

2x = 64

x = 32

∠5 = 32, ∠4 = 32

∠6 + 136 = 180 (because straight line)

∠6 = 44

∠7 + ∠6 + 47 = 180 (because triangle)

∠7 + 44 + 47 = 180

∠7 = 180 - 91

∠7 = 89