IN rhombus ABCD, measure of angle DAB equals two times the measure of angle ADC and CB equals 6. Find measure of angle ACD

Answer 1

Opposite angles of a rhombus are equal are equal. The sum of rhombus angles is 360.

Let angle DAB = angle BCD = a
Then angle ADC = angle ABC = a/2
3a = 360
a = 120
The rhombus internal angles are 120 (twice) and 60 (twice).

ACD is not a rhombus angle. AC is a diagonal, with length 6. ACD is the angle between diagonal AC and side CD. Draw the figure and you will see that ACD is 60 degrees.

It makes no difference what side CD is. That information was not required.