what is the value of x in the figure?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In triangle ABC, we know two angles and want to find the third - angle related to x.

Step2: Calculate the angle at ∠ACB

In triangle ABC, let ∠A = 101°, ∠ABC=32°. Using the angle - sum property of a triangle (∠A+∠ABC + ∠ACB=180°), we can find ∠ACB. ∠ACB=180°−101° - 32° ∠ACB = 47°

Step3: Consider the properties of a parallelogram

Since AB = CD = 4.7 and AD = BC = 3.4, ABCD is a parallelogram. In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Also, we know that ∠ACB and x are part of the angle - relationships in the parallelogram. In triangle BCD, we know that the angle adjacent to ∠ACB in the parallelogram is related to x. Since the sum of angles in triangle BCD is also 180°, and we know the side - length relationships, and considering the angle - sum property in triangle ABC which we calculated in Step 2. We know that x = 47°

Answer:

47°