Question

problem 21: (first taught in lesson 42) find x. after you enter your answer press go. x =

Explanation:

Step1: Use the property of a rhombus

In a rhombus, the diagonals bisect the angles. Also, adjacent angles in a rhombus are supplementary. But here, we can use the triangle angle - sum property. The two triangles formed by the diagonal are congruent. Let's consider one of the triangles. The sum of angles in a triangle is \(180^{\circ}\).

Step2: Calculate \(x\)

We know that in a rhombus, the diagonal bisects the angle. Let's assume the triangle formed by the sides of the rhombus and the diagonal. We have \(x + x+96^{\circ}=180^{\circ}\) (sum of angles in a triangle). Combine like terms: \(2x=180^{\circ}-96^{\circ}\). So, \(2x = 84^{\circ}\). Then \(x=\frac{84^{\circ}}{2}\).

Answer:

\(42\)