Question

determining whether a figure is a parallelogram
10 in.
(x + 5) in.
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.
(2x - 3) in.
(x + 2) in.

Explanation:

Step1: Set up equations for opposite - sides equality

In a parallelogram, opposite sides are equal. So we set up two equations:
Equation 1: $2x - 3=10$ and Equation 2: $x + 5=x + 2$ (the second one is incorrect, we should use $x + 5$ and $x + 2$ in the correct way). The correct pairs of opposite - side equations are $2x-3 = x + 5$ and $10=x + 2$.
Solve $2x-3=x + 5$:
$2x-x=5 + 3$
$x = 8$.
Solve $10=x + 2$:
$x=10 - 2=8$.

Step2: Check if both pairs of opposite sides are equal with the found value of $x$

If $x = 8$, then for the first pair of opposite sides:
$2x-3=2\times8-3=16 - 3=13$ and $x + 5=8 + 5=13$.
For the second pair of opposite sides:
$x + 2=8+2 = 10$ and the other side is 10.
Since both pairs of opposite sides are equal, the figure could be a parallelogram.

Answer:

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