Find Angle DAC in a Deltoid: Using 2x and 60° Relationships

As we know that ABCD is a deltoid, and AC is the bisector of an angle and therefore:

$BAC=CAD=2X$

Now we focus on the triangle BAD and calculate the sum of the angles since we know that the sum of the angles in a triangle is 180 degrees:

$2X+2X+2X+60=180$

$6X+60=180$

$180-60=6X$

$120=6X$

We divide the two sections by 6:$\frac{120}{6}=\frac{6x}{6}$

$20=x$

Now we can calculate the angle DAC:

$20\times2=40$