15. In \( \triangle A B C \), if \( m \angle A \) is thirteen less than \( m \angle C \) and \( m \angle B \) is eleven less than four times \( m \angle C \), find the measure of each angle. \[ \begin{array}{l}m \angle A= \\ m \angle B= \\ m \angle C=\end{array} \]

Let \( m \angle C = x \). According to the problem, we have: - \( m \angle A = x - 13 \) - \( m \angle B = 4x - 11 \) Since the sum of the angles in a triangle is always \( 180^\circ \), we can write the equation: \[ m \angle A + m \angle B + m \angle C = 180^\circ \] Substituting in our expressions for \( m \angle A \) and \( m \angle B \): \[ (x - 13) + (4x - 11) + x = 180 \] Combining like terms: \[ 6x - 24 = 180 \] Adding 24 to both sides: \[ 6x = 204 \] Dividing both sides by 6: \[ x = 34 \] Now we can find each angle: \[ m \angle C = x = 34^\circ \] \[ m \angle A = x - 13 = 34 - 13 = 21^\circ \] \[ m \angle B = 4x - 11 = 4(34) - 11 = 136 - 11 = 125^\circ \] Thus, the measures of the angles are: \[ \begin{array}{l} m \angle A= 21^\circ \\ m \angle B= 125^\circ \\ m \angle C= 34^\circ \end{array} \]