Question

based on the measures shown, could the figure be a parallelogram? 10 in. (x + 5) in. yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in. (2x - 3) in. (x + 2) in. yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in.

Explanation:

Step1: Set up equations for opposite sides

In a parallelogram, opposite sides are equal. So we have two equations:

1. \(2x - 3=x + 5\) (for one pair of opposite sides)
2. \(x+2 = 10\) (for the other pair of opposite sides)

Solve \(x + 2=10\)

Subtract 2 from both sides:
\(x=10 - 2\)
\(x = 8\)

Substitute \(x = 8\) into \(2x-3\) and \(x + 5\)

For \(2x-3\): \(2\times8-3=16 - 3=13\)
For \(x + 5\): \(8+5 = 13\)

Answer:

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