Answer: [tex]\angle CAD = 83^\circ [/tex] Option D
Step-by-step explanation:
In this question we use properties of parallelogram and angle sum property of a triangle.
In parallelogram ABCD
[tex] \angle ABC=40^\circ [/tex]
As, we know that opposite angles of parallelogram are equal
Therefore,
[tex] \angle ABC =\angle ADC =40^\circ [/tex]
Now, in triangle ADC
We know that sum of all the angles of a triangle is [tex]=180^\circ[/tex]
[tex]\angle ACD +\angle ADC +\angle DAC =180^\circ[/tex]
[tex]57^\circ +40^\circ +\angle DAC =180^\circ[/tex]
[tex]97^\circ + \angle DAC = 180^\circ [/tex]
Subtracting 97 from both sides we get
[tex] \angle DAC = 180^\circ - 97^\circ [/tex]
[tex] \angle DAC = 83^\circ [/tex]
Measure of [tex]\angle CAD = 83^\circ [/tex]
