Question

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

( x = )

Explanation:

Step1: Use the property of parallelogram

In a parallelogram \(ABCD\), \(AB = CD = 4.7\), \(BC=AD = 3.5\).

Step2: Use the ASA (Angle - Side - Angle) congruence criterion

\(\triangle ABC\cong\triangle CDB\) (by \(SSS\) criterion since \(AB = CD\), \(BC = AD\), \(AC=BD\)).
So, \(\angle CBD=\angle ACB\) (alternate - interior angles).

Step3: Use the angle - sum property of a triangle

In \(\triangle ABC\), we know that the sum of angles in a triangle is \(180^{\circ}\). But more simply, since \(AB\parallel CD\), we use the property of alternate - interior angles.
We know that in \(\triangle ABC\) and \(\triangle CDB\) (congruent triangles), and using the property of parallel lines \(AB\parallel CD\) and transversal \(CB\).
The angle \(x = 30^{\circ}\) (alternate - interior angles, because \(AB\parallel CD\) and \(CB\) is a transversal, and \(\triangle ABC\cong\triangle CDB\) (by \(SSS:AB = CD = 4.7\), \(BC = BC\) (common side), \(AC = BD=3.5\))

Answer:

\(30\)