The diagonals of rhombus ABCD intersect at E. Given that m∠CAD=20° and CE=4, find the m∠BCA.

BCA = 20 degrees

Step-by-step explanation:

A rhombus is an equilateral quadrilateral, with all four of its sides having the same length. In addition to that, one important geometric property that will really help us with this problem is the fact that the opposite sides of a rhombus are parallel.

This means that BC ||AD.

Consequently, because  BC ||AD,

m∠CAD = m∠BCA.

This is because they are alternate angles.

The alternate angle equality can be used in geometrical problems where you detect two parallel lines cut across by a transversal. in this, our case, the parallel lines BC and AD were transversed by AC.

This makes m∠CAD = m∠BCA because they are alternate angles)