Question

math 2 unit 2 quiz review
name: thiago gonzalez
use the picture to the right to answer questions 1 - 4. list all angle pairs

1. which angles are corresponding angles?
2. which angles are consecutive exterior?
3. which angles are linear pairs?
4. which angles are alternate interiors?
5. given that line m and line n are parallel, find all angle measures.

Explanation:

Step1: Recall corresponding - angles definition

Corresponding angles are in the same relative position. For parallel lines \(AB\) and \(CD\) cut by transversal \(FE\), the pairs are \(\angle1\) and \(\angle3\), \(\angle2\) and \(\angle4\), \(\angle5\) and \(\angle7\), \(\angle6\) and \(\angle8\).

Step2: Recall consecutive - exterior - angles definition

Consecutive exterior angles are outside the parallel lines and on the same - side of the transversal. The pairs are \(\angle1\) and \(\angle7\), \(\angle2\) and \(\angle8\).

Step3: Recall linear - pairs definition

Linear pairs are adjacent angles that form a straight - line. The pairs are \(\angle1\) and \(\angle2\), \(\angle3\) and \(\angle4\), \(\angle5\) and \(\angle6\), \(\angle7\) and \(\angle8\).

Step4: Recall alternate - interior - angles definition

Alternate interior angles are between the parallel lines and on opposite sides of the transversal. The pairs are \(\angle2\) and \(\angle7\), \(\angle3\) and \(\angle6\).

Step5: For the second figure, use angle - relationships for parallel lines

If a line is parallel to another line and we have an angle of \(125^{\circ}\). Let's assume the \(125^{\circ}\) angle and \(\angle1\) are corresponding angles. Then \(\angle1 = 125^{\circ}\). Since \(\angle1\) and \(\angle2\) are a linear pair, \(\angle2=180 - 125=55^{\circ}\). Corresponding angles are equal, vertical angles are equal. So \(\angle3=\angle1 = 125^{\circ}\), \(\angle4=\angle2 = 55^{\circ}\), \(\angle5=\angle1 = 125^{\circ}\), \(\angle6=\angle2 = 55^{\circ}\), \(\angle7=\angle3 = 125^{\circ}\), \(\angle8=\angle4 = 55^{\circ}\).

Answer:

1. \(\angle1\) and \(\angle3\), \(\angle2\) and \(\angle4\), \(\angle5\) and \(\angle7\), \(\angle6\) and \(\angle8\)
2. \(\angle1\) and \(\angle7\), \(\angle2\) and \(\angle8\)
3. \(\angle1\) and \(\angle2\), \(\angle3\) and \(\angle4\), \(\angle5\) and \(\angle6\), \(\angle7\) and \(\angle8\)
4. \(\angle2\) and \(\angle7\), \(\angle3\) and \(\angle6\)
5. The angles are \(125^{\circ}\) and \(55^{\circ}\) where the angle corresponding to the \(125^{\circ}\) given angle and its vertical - angle and corresponding - angles are \(125^{\circ}\), and the linear - pair angles and their vertical - angles are \(55^{\circ}\).