Final Answer:
The measures of the numbered angles are as follows: \( m∠1 = m∠5 = m∠7 = 76° \), \( m∠2 = m∠6 = m∠8 = 180° - 76° = 104° \), \( m∠4 = m∠n \) are not specified, and the value of \( m \) is not provided.
Step-by-step explanation:
To determine the measures of the numbered angles, we first recognize that angles on a straight line sum up to \(180°\). Angle \( m∠3 \) is not mentioned, so we can express the sum of angles on one side of the straight line as \( m∠1 + m∠2 + 76° + m∠4 + m + m∠6 \). Since this sum equals \(180°\), we can solve for \( m∠2 \), \( m∠6 \), and \( m∠4 \), obtaining \( m∠2 = m∠6 = m∠8 = 104° \).
The specific values for \( m∠4 \) and \( m∠n \) are not given. The measure of \( m∠4 \) can be determined if \( m \) is provided. The value of \( m \) is not given in the question, so \( m∠4 \) remains unspecified. Similarly, \( m∠n \) is not specified, and its measure is left open-ended.
In conclusion, without additional information about \( m \) or \( m∠n \), the measures of \( m∠1 \), \( m∠5 \), \( m∠7 \) are \(76°\), and the measures of \( m∠2 \), \( m∠6 \), \( m∠8 \) are \(104°\). The values for \( m∠4 \) and \( m∠n \) are not determined with the information provided.