1. **State the problem:** We have a triangle with angles $49^\circ$, $2a - 45^\circ$, and $2a$. We need to find the value of $a$. 2. **Recall the Triangle Angle-Sum Theorem:** The sum of the interior angles of a triangle is always $180^\circ$. 3. **Set up the equation:** $$49 + (2a - 45) + 2a = 180$$ 4. **Simplify the equation:** $$49 + 2a - 45 + 2a = 180$$ $$4a + 4 = 180$$ 5. **Solve for $a$:** $$4a = 180 - 4$$ $$4a = 176$$ $$a = \frac{176}{4} = 44$$ **Final answer:** $a = 44$