Question

the figure below is a rhombus. find the value of x. 48° x = ?°

Explanation:

Step1: Recall rhombus diagonal properties

In a rhombus, diagonals bisect the angles and are perpendicular to each other. Also, the triangles formed by the diagonals are right - angled triangles. In a right - angled triangle, the sum of the two non - right angles is \(90^{\circ}\).
We know one of the non - right angles is \(48^{\circ}\), and we need to find the other non - right angle \(x\).

Step2: Calculate the value of \(x\)

Using the property that in a right - angled triangle, if one acute angle is \(a\) and the other is \(b\), then \(a + b=90^{\circ}\).
Here, \(a = 48^{\circ}\) and \(b=x\). So, \(x=90^{\circ}- 48^{\circ}\)
\(x = 42^{\circ}\)

Answer:

\(42\)