1. **State the problem:** We are given a circle with center A and points L, B, Q, G, and M on or around the circle. We know the measures of angles $\angle MLG = 20.45^\circ$ and $\angle QB = 25.5^\circ$. We need to find the measure of $\angle MG$. 2. **Identify the relevant properties:** In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Also, angles subtended by the same chord or arc are equal. 3. **Analyze the given angles:** $\angle MLG$ is an inscribed angle intercepting arc $MG$. Therefore, the measure of arc $MG$ is $2 \times 20.45^\circ = 40.9^\circ$. 4. **Use the given $\angle QB = 25.5^\circ$:** This angle likely relates to another arc or chord in the circle, but since the problem asks for $\angle MG$, we focus on the arc $MG$ intercepted by $\angle MLG$. 5. **Determine $m\angle MG$:** If $\angle MG$ is the angle at point M subtended by chord $AG$ or related to arc $LG$, we use the fact that the measure of an inscribed angle is half the intercepted arc. Since $\angle MLG$ intercepts arc $MG$ of $40.9^\circ$, $\angle MG$ is equal to $20.45^\circ$ if it is the same inscribed angle or related by symmetry. 6. **Final answer:** $m\angle MG = 20.45^\circ$.