1. **State the problem:** We are given three parallel horizontal lines intersected by a vertical line and a slanting line forming multiple labeled angles. We need to find the missing angle measures. 2. **Given angles:** \(m\angle 4 = 18^\circ\), \(m\angle 3 = 62^\circ\), an adjacent angle of \(68^\circ\) next to \(\angle 3\), and an angle of \(85^\circ\) near the bottom-right intersecting the slanting line. 3. **Find missing angles formed by the vertical line:** - At the middle horizontal line, angles \(\angle 3 = 62^\circ\) and its adjacent angle \(68^\circ\). Since adjacent angles on a straight line sum to \(180^\circ\), check: \(62^\circ + 68^\circ = 130^\circ\), so the straight line must be forming angles with the vertical line. This suggests \(m\angle 5 = 180^\circ - 62^\circ = 118^\circ\). - \(m\angle 1\) and \(m\angle 2\) are corresponding or alternate interior angles with \(m\angle 3\) and \(m\angle 4\), so - \(m\angle 1 = m\angle 3 = 62^\circ\) - \(m\angle 2 = m\angle 4 = 18^\circ\) - Similar reasoning applies for \(m\angle 6\) and \(m\angle 7\) at the top intersecting the slanting line. 4. **Find angles on the slanting line intersecting the parallel lines:** - Given \(m\angle 8 + m\angle 9 + 85^\circ = 180^\circ\) along a straight line. - Assuming \(m\angle 8 = m\angle 2 = 18^\circ\) by corresponding angles. - Then \(m\angle 9 = 180^\circ - 85^\circ - 18^\circ = 77^\circ\). 5. **Determine \(m\angle 10, m\angle 11, m\angle 12, m\angle 13\):** - \(m\angle 10\) and \(m\angle 11\) are adjacent vertical angles with \(m\angle 9\) and \(m\angle 8\), so they equal corresponding angles. - Therefore, - \(m\angle 10 = m\angle 3 = 62^\circ\) - \(m\angle 11 = m\angle 4 = 18^\circ\) - \(\angle 12\) and \(\angle 13\) near the top of the slanting line correspond to \(\angle 1 = 62^\circ\) and \(\angle 5 = 118^\circ\). **Final answers:** \(m\angle 1 = 62^\circ\) \(m\angle 2 = 18^\circ\) \(m\angle 3 = 62^\circ\) \(m\angle 4 = 18^\circ\) \(m\angle 5 = 118^\circ\) \(m\angle 6 = 62^\circ\) \(m\angle 7 = 18^\circ\) \(m\angle 8 = 18^\circ\) \(m\angle 9 = 77^\circ\) \(m\angle 10 = 62^\circ\) \(m\angle 11 = 18^\circ\) \(m\angle 12 = 62^\circ\) \(m\angle 13 = 118^\circ\)