1. **State the problem:** We are given a triangle with two angles labeled as $2m - 3^\circ$ and $m + 6^\circ$. We need to find the value of $m$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always $180^\circ$. So, $$ (2m - 3) + (m + 6) + \text{third angle} = 180 $$ 3. **Find the third angle:** Since the third angle is not given, we can express it as: $$ \text{third angle} = 180 - [(2m - 3) + (m + 6)] $$ 4. **Simplify inside the brackets:** $$ (2m - 3) + (m + 6) = 2m + m - 3 + 6 = 3m + 3 $$ 5. **Substitute back:** $$ \text{third angle} = 180 - (3m + 3) = 180 - 3m - 3 = 177 - 3m $$ 6. **Since the triangle has three angles, the sum is 180, so the third angle must be positive and less than 180.** 7. **If the problem asks to find $m$ such that the triangle is valid, we can set the third angle to be positive:** $$ 177 - 3m > 0 \implies 177 > 3m \implies m < 59 $$ 8. **Alternatively, if the problem expects the third angle to be equal to a specific value or if the triangle is equilateral or isosceles, more information is needed.** Since the problem only gives these two angles, the main step is to express the third angle in terms of $m$ and understand the constraints. **Final expression for the third angle:** $$ \boxed{177 - 3m} $$ **Summary:** The three angles are $2m - 3^\circ$, $m + 6^\circ$, and $177 - 3m^\circ$, and they sum to $180^\circ$.