Question

given rhombus tuvw. find m∠4.

Explanation:

Step1: Recall the properties of a rhombus

In a rhombus, the diagonals are perpendicular bisectors of each other. So, the four triangles formed by the diagonals are right - angled triangles.

Step2: Use the angle - sum property of a triangle

In right - triangle \(VWT\), we know that one angle is \(28^{\circ}\) and the right - angle is \(90^{\circ}\). Using the angle - sum property of a triangle (\(\angle1+\angle VWT+\angle WTV = 180^{\circ}\)), and since \(\angle VWT = 90^{\circ}\), we can find \(\angle1\). But also, in a rhombus, the diagonals bisect the angles of the rhombus. Another way is to note that in a rhombus, adjacent angles are supplementary. But for the triangle formed by the diagonals:
We know that in a right - triangle (formed by the diagonals of the rhombus), if one of the non - right angles is \(28^{\circ}\), then \(\angle4=90^{\circ}-28^{\circ}\)

Answer:

\(62^{\circ}\)