1. The problem asks to find the value of angle $b$ in a triangle where two angles are given: $38^\circ$ and $101^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always $180^\circ$. 3. Using the formula: $$b + 38^\circ + 101^\circ = 180^\circ$$ 4. Combine the known angles: $$b + 139^\circ = 180^\circ$$ 5. Subtract $139^\circ$ from both sides to isolate $b$: $$b = 180^\circ - 139^\circ$$ 6. Calculate the difference: $$b = 41^\circ$$ Therefore, the value of angle $b$ is $41^\circ$.