Answer to Question #94815 in Geometry for Zaden

Question

In parallelogram ABCD, m ∠ A= 56.58 degrees. Explain how you would find the other angle measures of ABCD." Please help.

Answer 1

Consider the triange ABH. It is right triangle. Then angle A + angle ABH = 90 degrees. If angle A = 56.58 degress, then angle ABH = 90-56.58 = 33.42 degrees.
Angle B = Angle ABH + Angle HBC=33.42(degrees)+ 90(degrees) = 123.42 degrees

Now consider triangles ABC and ADC.
We know that AB = CD and AD = BC because ABCD is parallelogram
then we can say that triangle ABC = triangle ADC. Therefore, angle D = angle B = 123.42 degrees; 
angle BCA = angle CAD and angle BAC = angle ACD.
angle A = angle BAC + angle CAD
angle C = angle BCA + angle ACD
Thus, angle C = angle A = 56.68 degrees.