Answer
$OP=7$, $MN=23$
Work Step by Step
Theorem 4.4.3: The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases.
$\frac{base+base}{2}=median$
$\frac{(3x+2)+(2x-7)}{2}=15$
Combine like terms in the numerator...
$\frac{5x-5}{2}=15$
Multiply both sides by 2...
$5x-5=30$
Add 5 to both sides...
$5x=35$
Divide both sides by 5...
$x=7$
$MN=3x+2=3(7)+2=23$
$OP=2x-7=2(7)-7=7$
