The angle ABC and angle CDA are both equal to 56 degrees.
To find angle ABC and angle CDA in figure ABCD, we can start by using the fact that side AB is equal to side AD and side BC is equal to side CD. Since angle BAD is given as 44 degrees and angle BCD is given as 80 degrees, we can use the triangle angle sum property to find angle ABC and angle CDA.
Using the triangle angle sum property, we know that the sum of angles in a triangle is always 180 degrees.
So, in the triangle ABC, angle ABC + angle BAC + angle BCA = 180 degrees.
Since angle BAC and angle BCA are equal to angle BAD and angle BCD respectively, we can substitute the given values and solve for angle ABC:
angle ABC + 44 degrees + 80 degrees = 180 degrees
angle ABC + 124 degrees = 180 degrees
angle ABC = 180 degrees - 124 degrees = 56 degrees
Similarly, in triangle CDA, angle CDA + angle DAC + angle DCA = 180 degrees.
Since angle DAC is equal to angle BAD and angle DCA is equal to angle BCD, we can substitute the given values and solve for angle CDA:
angle CDA + 44 degrees + 80 degrees = 180 degrees
angle CDA + 124 degrees = 180 degrees
angle CDA = 180 degrees - 124 degrees = 56 degrees