Question

the figure below is a rhombus. find the value of x. 58° x = ?°

Explanation:

Step1: Recall rhombus properties

In a rhombus, diagonals are perpendicular bisectors and bisect the angles. Also, the sum of angles in a triangle is \(180^\circ\). The triangle with \(58^\circ\) angle is a right triangle (since diagonals are perpendicular) at the intersection point.

Step2: Calculate \(x\)

In the right triangle, one angle is \(90^\circ\), another is \(58^\circ\). So \(x = 180^\circ - 90^\circ - 58^\circ\)
\(x = 32^\circ\)

Answer:

\(32\)