Answer:
Using properties of parallelogram and angle sum property of a triangle in the figure as shown below in the attachment
In parallelogram ABCD, AC is a diagonal.
Given: [tex]\angle ABC = 40^{\circ}[/tex] and [tex]\angle ACD= 57^{\circ}[/tex]
As, we know that opposite angles in parallelogram are equal.
therefore,
[tex]\angle ABC =\angle ADC= 40^{\circ}[/tex]
Now, in ΔADC
Sum of the measures of angles in a triangle is 180 degree.
[tex]\angle ACD+ \angle ADC+\angle DAC =180^{\circ}[/tex]
Substituting the values of [tex]\angle ADC= 40^{\circ}[/tex] and [tex]\angle ACD= 57^{\circ}[/tex] we have;
[tex]57^{\circ}+40^{\circ}+\angle DAC =180^{\circ}[/tex]
or
[tex]97^{\circ}+\angle DAC =180^{\circ}[/tex]
Subtract [tex]97^{\circ}[/tex] from both sides we get
[tex]\angle DAC =180 -97 =83^{\circ}[/tex]
Therefore, the measure of angle CAD is [tex]83^{\circ}[/tex].
