In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to 180 degrees).
Given the angles in the parallelogram:
- \( m \angle L = 9x + 10 \)
- \( m \angle J = 10x + 2 \)
Since angles \( L \) and \( J \) are adjacent, we can set up the equation:
\[ m \angle L + m \angle J = 180 \]
Substituting the expressions for the angles, we get:
\[ (9x + 10) + (10x + 2) = 180 \]
Combining like terms:
\[ 19x + 12 = 180 \]
Subtracting 12 from both sides:
\[ 19x = 168 \]
Dividing by 19:
\[ x = \frac{168}{19} \approx 8.842 \]
Now, we can find \( m \angle M \), which is equal to \( m \angle L \):
\[ m \angle L = 9x + 10 \]
Substituting the value of \( x \):
\[ m \angle L = 9\left(\frac{168}{19}\right) + 10 = \frac{1512}{19} + 10 \]
Converting 10 to a fraction with a denominator of 19:
\[ 10 = \frac{190}{19} \]
Now combine:
\[ m \angle L = \frac{1512}{19} + \frac{190}{19} = \frac{1702}{19} \]
Calculating this gives approximately:
\[ m \angle L \approx 89.579 \quad (\text{rounded to two decimal places}) \]
Since the calculated angle doesn't match exactly one of your given options, let’s check with the options you provided to ensure \( L \) and \( M \) can fit one of these measurements given that they should be equal.
Since we need \( m \angle M \):
- \( m \angle M = m \angle L \) which is very close to 90 degrees.
If the angles we calculated were incorrect due to simplification, please provide further details or an explicit structure of how they relate to \( 98, 72, 55, 100 \).
However, based on the original calculations and adjacent relationships:
- The possible measured angles are \( 98, 72, 55, \) or \( 100 \).
From the calculations, no exact matching number arises. If we incorrectly processed the angles or if additional values are in effect, correct that and proceed with reviewing either calculations or importance of \( x \). Based on problem settings, the closest potential answer is not appearing.
Essentially: Please revise angle definitions or condition settings to match one of these options conclusively.
Ensure you check the assumptions lying out concerning angles and verification sets pointing towards numerical settings provided \( 96 \) and approximate returns would most often yield one core relationship for \( L \) to fall nearly toward common degrees.