check my answer

We  can use  the Law of Cosines to  find the measure of the smaller angle...we have that

2.9^2  = 4^2 + 4^2  - 2 (4 * 4)  cos  (smaller angle in the rhombus)

Simplify

[ 2.9^2  -4^2 - 4^2 ]  /  [-2 (4 * 4)]  = cos (smaller angle in the rhombus)

Using the arccos  we  have  that

arccos ( [ 2.9^2  -4^2 - 4^2 ]  /  [-2 (4 * 4)] )  =  smaller angle in the rhombus ≈  42.51°

The larger angle in the rhombus  will be supplemental to this = 137.49°  = 137.5°

LOOKS LIKE YER ON A ROLL  !!!

Let rhombus side be       c = 4

1/2 of short diagonal       a = 1.45

1/2 of long  diagonal        b = ?

We have the right triangle  

Larger angle  β = ?                    cos(β/2) = a / c =68.74619°

                                                              β = 137.4923816°     

IT IS TOTALLY______

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