1. **State the problem:** We have a circle centered at point $D$ with points $A$, $B$, and $C$ on it in clockwise order. We know the angles at the center: $\angle ADB = 7N + 12$, $\angle ADC = 13N - 16$, and $\angle BDC = 6N$. We want to find the measure of the major arc $\stackrel{\large{\frown}}{BAC}$ in degrees. 2. **Understand the given information:** Since $A$, $B$, and $C$ lie on the circle and $D$ is the center, the angles $\angle ADB$, $\angle BDC$, and $\angle ADC$ are central angles corresponding to arcs $AB$, $BC$, and $AC$ respectively. 3. **Check the sum of angles:** The central angles around point $D$ should sum to $360^\circ$ because they represent the full circle. $$ (7N + 12) + (6N) + (13N - 16) = 360 $$ Simplify: $$ 7N + 12 + 6N + 13N - 16 = 360 $$ $$ (7N + 6N + 13N) + (12 - 16) = 360 $$ $$ 26N - 4 = 360 $$ 4. **Solve for $N$:** $$ 26N = 360 + 4 $$ $$ 26N = 364 $$ $$ N = \frac{364}{26} = 14 $$ 5. **Calculate each angle:** $$ \angle ADB = 7N + 12 = 7(14) + 12 = 98 + 12 = 110^\circ $$ $$ \angle BDC = 6N = 6(14) = 84^\circ $$ $$ \angle ADC = 13N - 16 = 13(14) - 16 = 182 - 16 = 166^\circ $$ 6. **Find the arc measure of major arc $\stackrel{\large{\frown}}{BAC}$:** - The minor arcs corresponding to $\angle ADB$ and $\angle BDC$ are arcs $AB$ and $BC$. - The minor arc $AC$ corresponds to $\angle ADC$. Since $A$, $B$, and $C$ are in clockwise order, major arc $BAC$ includes arcs $AB$ and $BC$, so its arc measure is: $$ 110^\circ + 84^\circ = 194^\circ $$ Hence, the major arc $\stackrel{\large{\frown}}{BAC}$ measures $194$ degrees. **Final answer:** The measure of the major arc $\stackrel{\large{\frown}}{BAC}$ is $194^\circ$.