1. The problem asks to find the value of $m_1$ using the given diagram where $m=8$ and an angle of 48 degrees is shown. 2. Since the diagram is not visible, we assume this is a problem involving angles and possibly the use of angle relationships such as complementary, supplementary, or angles in polygons. 3. If $m=8$ represents a multiplier or a segment length and the angle 48 degrees is related to $m_1$, we need to use the relationship given or implied by the diagram. 4. Without the diagram, a common approach is to use the fact that angles around a point sum to 360 degrees or angles on a straight line sum to 180 degrees. 5. If $m_1$ is an angle adjacent to 48 degrees and they form a straight line, then: $$m_1 + 48 = 180$$ 6. Solving for $m_1$: $$m_1 = 180 - 48$$ $$m_1 = 132$$ 7. Therefore, the value of $m_1$ is 132 degrees. This solution assumes the angle $m_1$ and 48 degrees are supplementary based on typical angle problems.