We find the slope of AB using the slope formula:



We find the slope of AD using the slope formula:



Then we use the formula for the tangent of the angle between two lines
AB and AD:







Multiply every term in the top and bottom by LCD=6









This formula will give either the tangent of the acute or obtuse angle
between two lines, which are supplementary, depending on our choice for
m1 and m2.  The tangents of the acute and obtuse angles between two lines
are different only by their signs.

Since A is acute, tan(A) = 1 and m∠A = 45°

Since the opposite interior angles of a parallelogram are equal in measure,

m∠C = 45°

Since adjacent interior angles of a parallelogram are supplementary,

m∠B = 180°-45° = 135° and since ∠D is opposite ∠B, m∠D also = 135°.

Edwin