Question

m∠jml = 70° and jklm is a rhombus, solve for the variables.
hint about rhomubs

Explanation:

Step1: Properties of rhombus diagonals

In a rhombus, the diagonals are perpendicular bisectors of each other. So, \(z = 90^{\circ}\). Also, the diagonals bisect the angles of the rhombus.

Step2: Find \(x\)

Since \(m\angle JML=70^{\circ}\) and the diagonal \(MK\) bisects \(\angle JML\) (property of rhombus diagonals), then \(x = 20^{\circ}\) (because \(\angle JML = 70^{\circ}\) and in right - triangle formed by half - angles and right - angle, \(x=90 - 70=20\)).

Step3: Use symmetry property

In a rhombus, the angles opposite to each other are equal and the diagonals bisect the angles. By the symmetry of the rhombus (the diagonals bisect the angles of the rhombus), \(y=x = 20^{\circ}\)

Answer:

\(x = 20\), \(y = 20\), \(z = 90\)