Question

determining whether a figure is a parallelogram
based on the measures shown, could the figure be a parallelogram?
yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in.
yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.
no, there are three different values for x when each expression is set equal to 10.
no, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

Explanation:

Step1: Set \(x + 5=2x - 3\)

Solve for \(x\):
\(x+5 = 2x - 3\)
\(5 + 3=2x - x\)
\(x = 8\)

Step2: Substitute \(x = 8\) into \(x + 2\)

\(x+2=8 + 2=10\)

Step3: Check if it's a parallelogram

If \(x = 8\), sides are \(10\), \(13\), \(13\), \(10\). But for a parallelogram, opposite sides must be equal. If we assume \(10\) and \(10\) as one pair, and \(x + 5\) and \(2x - 3\) as the other pair. When \(x = 8\), \(x + 5=13\) and \(2x - 3 = 13\). But if we set \(x+2 = 10\) (i.e., \(x = 8\)), then \(x + 5=13\) and \(2x - 3=13\). But if we consider the property of parallelogram (opposite sides equal), if we set \(10\) as one side, solving \(x+5 = 10\) gives \(x = 5\), then \(2x - 3=7\) and \(x + 2 = 7\). But \(7
eq10\). The value of \(x\) that makes one pair of sides congruent (\(x = 8\) for \(10\) and \(10\) with \(13\) and \(13\) not in the right pairs; or \(x = 5\) for wrong side - pair equality) does not make the other pair of sides congruent in the correct opposite - side sense.

Answer:

Yes, one pair of opposite sides could measure \(10\) in., and the other pair could measure \(13\) in.