Question

what is the value of ( x ) in the figure?

Explanation:

Step1: Use the property of congruent triangles

In the figure, \(AB = CD = 4.3\), \(AC = BD = 3.9\), and \(BC\) is common. So, \(\triangle ABC\cong\triangle DCB\) (by SSS - Side - Side - Side congruence criterion).

Step2: Find the angle in \(\triangle ABC\)

In \(\triangle ABC\), using the angle - sum property of a triangle (\(\angle A+\angle ABC+\angle ACB = 180^{\circ}\)). We know \(\angle A=110^{\circ}\), \(\angle ABC = 33^{\circ}\). Then \(\angle ACB=180^{\circ}-(110^{\circ}+33^{\circ})=37^{\circ}\).

Step3: Use the congruent - triangle angle property

Since \(\triangle ABC\cong\triangle DCB\), \(\angle x=\angle ACB\) (corresponding angles of congruent triangles).

Answer:

\(37\)