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 measur of each angle. \[ m \angle J= \] \[ M \angle K= \] O Gina Wilson (All Things Algebra), 201

Let \( m \angle J = x \). According to the problem, we have: \[ m \angle K = x + 9 \] \[ m \angle L = 2x - 21 \] Using the triangle angle sum property, we know that the sum of the angles in a triangle is 180 degrees: \[ x + (x + 9) + (2x - 21) = 180 \] Combining like terms: \[ 4x - 12 = 180 \] Adding 12 to both sides: \[ 4x = 192 \] Dividing by 4: \[ x = 48 \] Now we can find each angle: \[ m \angle J = x = 48^\circ \] \[ m \angle K = x + 9 = 57^\circ \] \[ m \angle L = 2x - 21 = 75^\circ \] Thus, the measures of the angles are: \[ m \angle J = 48^\circ \] \[ m \angle K = 57^\circ \] \[ m \angle L = 75^\circ \]