16. In \( \triangle J K L \), if \( m \angle K \) is nine more than \( m \angle J \) and \( m \angle L \) is 21 less than twice \( m \angle J \), find the measure of each angle. \begin{tabular}{l}\( m \angle J= \) \\ \( m \angle K= \) \\ \( m \angle L= \) \\ \hline\end{tabular}

Let's denote the measure of angle \( J \) as \( x \). According to the problem, we can express the other two angles in terms of \( x \): - The measure of angle \( K \) can be expressed as \( m \angle K = x + 9 \). - The measure of angle \( L \) can be expressed as \( m \angle L = 2x - 21 \). In a triangle, the sum of the interior angles is always 180 degrees. Therefore, we can write the equation: \[ x + (x + 9) + (2x - 21) = 180 \] Combining like terms gives: \[ x + x + 9 + 2x - 21 = 180 \\ 4x - 12 = 180 \] Next, add 12 to both sides: \[ 4x - 12 + 12 = 180 + 12 \\ 4x = 192 \] Now divide by 4: \[ x = \frac{192}{4} \\ x = 48 \] Now that we have \( m \angle J \), we can find \( m \angle K \) and \( m \angle L \): \[ m \angle J = x = 48 \\ m \angle K = x + 9 = 48 + 9 = 57 \\ m \angle L = 2x - 21 = 2(48) - 21 = 96 - 21 = 75 \] So, the measures of the angles are: \[ \begin{tabular}{l} \( m \angle J = 48^\circ \) \\ \( m \angle K = 57^\circ \) \\ \( m \angle L = 75^\circ \) \\ \hline \end{tabular} \]