Question: User: Name: __________\nPeriod: 1\nDate: aa-28-26\n\nParallel Lines Cut by Transversal Practice\n\nFind the measurement of the following angles:\nm\angle1 125\nm\angle2 45\nm\angle3\nm\angle4\nm\angle5 125\nm\angle6\nm\angle7\nm\angle8\n\nThe diagram shows two parallel lines cut by a transversal.\nA. What kind of angle pair is formed by the two labeled angles?
1. **Problem Statement:** We have two parallel lines cut by a transversal, with some angles given: $m\angle1 = 125$, $m\angle2 = 45$, $m\angle5 = 125$. We need to find the measures of $m\angle3$, $m\angle4$, $m\angle6$, $m\angle7$, and $m\angle8$. Also, identify the type of angle pair formed by the two labeled angles (assumed $\angle1$ and $\angle5$).\n\n2. **Important Rules:**\n- When two parallel lines are cut by a transversal, corresponding angles are equal.\n- Alternate interior angles are equal.\n- Consecutive interior angles are supplementary (sum to 180).\n- Vertical angles are equal.\n\n3. **Find $m\angle3$:**\n$\angle1$ and $\angle3$ are vertical angles, so\n$$m\angle3 = m\angle1 = 125.$$\n\n4. **Find $m\angle4$:**\n$\angle2$ and $\angle4$ are vertical angles, so\n$$m\angle4 = m\angle2 = 45.$$\n\n5. **Find $m\angle6$:**\n$\angle5$ and $\angle6$ are vertical angles, so\n$$m\angle6 = m\angle5 = 125.$$\n\n6. **Find $m\angle7$:**\n$\angle6$ and $\angle7$ are supplementary (linear pair), so\n$$m\angle7 = 180 - m\angle6 = 180 - 125 = 55.$$\n\n7. **Find $m\angle8$:**\n$\angle7$ and $\angle8$ are vertical angles, so\n$$m\angle8 = m\angle7 = 55.$$\n\n8. **Type of angle pair formed by $\angle1$ and $\angle5$:**\nThey are corresponding angles because they are on the same side of the transversal and in corresponding positions relative to the parallel lines. Corresponding angles are equal when lines are parallel.\n\n**Final answers:**\n$$m\angle3 = 125,\quad m\angle4 = 45,\quad m\angle6 = 125,\quad m\angle7 = 55,\quad m\angle8 = 55.$$\n\nThe two labeled angles $\angle1$ and $\angle5$ form a pair of corresponding angles.