In rhombus defg, if m∠deg=19, find m∠eff
a) 142
b) 38
c) 71
d) 19

C) 71

Step-by-step explanation:

Just gonna list all the angles.

Rhombuses have congruent diagonals so that means the angle DEF and DGF are the same, as well as GDE and GFE are the same.

The lines cutting the rhombus into fourths also bisect the angles they cut through, which basically means since a line cuts DEF into two other angles, DEG and GEF, these two angles are the same.

Since it's a quadrilateral  all angles add up to 360 as well.  

Now, working with that we know DEG is 19, well DEG = GEF = 19, so DEF is 19*2=38.  Then DEF = DGF = 38.

We also know GDE + DEF + EFG + FGD = 360 = 38 + 38 + GDE + GFE.  Or in other words GDE + GFE = 284.  Then we also know GDE = GFE so that means that 284 has to be cut in half.  so GDE = GFE = 142.

Similarly GDF = EDF and GDF + EDF = GDE = 142 so GDF = EDF = 71.  A similar argument can be made for GFD and DFE.

You said you need EFD, which I labeled as DFE but anyway, with all that reasoning it's 71.

Let me know if you don't get how the properties of a rhombus work and I can explain if you want.