Question

in parallelogram ABCD, AC is diagonal, the measure <ABC is 40°, and the measure of <ACD IS 57°. what is the measure of &lt;CAD?

Answer 1

Answer: $\angle CAD = 83^\circ$ Option D

Step-by-step explanation:

In this question we use properties of parallelogram and angle sum property of a triangle.

In parallelogram ABCD

$\angle ABC=40^\circ$

As, we know that opposite angles of parallelogram are equal

Therefore,

$\angle ABC =\angle ADC =40^\circ$

Now, in triangle ADC

We know that sum of all the angles of a triangle is $=180^\circ$

$\angle ACD +\angle ADC +\angle DAC =180^\circ$

$57^\circ +40^\circ +\angle DAC =180^\circ$

$97^\circ + \angle DAC = 180^\circ$

Subtracting 97 from both sides we get

$\angle DAC = 180^\circ - 97^\circ$

$\angle DAC = 83^\circ$

Measure of $\angle CAD = 83^\circ$