Rhombus ABCD with ∠ABC = 56°. Find ∠ACD (angle between diagonal AC and side CD at C).

Introduction / Context:
Rhombi have equal sides, their diagonals bisect the vertex angles, and the diagonals are perpendicular. Using these facts allows us to compute angles made by a diagonal with a side.

Given Data / Assumptions:

• ABCD is a rhombus; ∠ABC = 56°.
• We seek ∠ACD, the angle between AC and CD at C.

Concept / Approach:
Adjacent angles in a parallelogram (hence in a rhombus) are supplementary. Also, diagonal AC bisects ∠C. Therefore, once ∠C is found, ∠ACD is half of ∠C.

Step-by-Step Solution:
∠B = 56° ⇒ adjacent angle ∠C = 180° − 56° = 124°.Diagonal AC bisects ∠C, so ∠ACD = 124° / 2 = 62°.

Verification / Alternative check:
Opposite angles in a rhombus are equal; the same logic from ∠A would yield matching bisected parts at C.

Why Other Options Are Wrong:
90° confuses with the fact that diagonals are perpendicular to each other, not necessarily to sides; 60° and 56° do not equal half of 124°.

Common Pitfalls:
Bistector applied to the wrong angle or assuming ∠C = ∠B in a rhombus (not true unless it is a square).

Final Answer:
62°