Question

parallel lines review
identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutive interior, vertical, or adjacent.
1)
2)
3)
4)
find the measure of each angle indicated.
5)
6)
7)
8)
solve for x.
9)
10)

Explanation:

Step1: Identify Angle Relationships (1 - 4)

• For 1): Angles \(x\) and \(y\) are adjacent (share a common side and vertex).
• For 2): Angles \(x\) and \(y\) are alternate exterior (outside the parallel lines and on opposite sides of the transversal).
• For 3): Angles \(x\) and \(y\) are corresponding (in the same relative position at each intersection).
• For 4): Angles \(x\) and \(y\) are alternate interior (inside the parallel lines and on opposite sides of the transversal).

Step2: Find Angle Measures (5 - 8)

• For 5): Using the linear - pair relationship (supplementary angles), if one angle is \(84^{\circ}\), then the indicated angle is \(180^{\circ}-84^{\circ}=96^{\circ}\).
• For 6): Using the property of parallel lines and a transversal (corresponding angles), the indicated angle is \(93^{\circ}\) (vertical angles are equal and then corresponding angles).
• For 7): Using the alternate interior angle property, the indicated angle is \(54^{\circ}\).
• For 8): Using the linear - pair relationship, if the adjacent angle is \(130^{\circ}\), then the indicated angle is \(180^{\circ}-130^{\circ}=50^{\circ}\).

Step3: Solve for \(x\) (9 - 10)

• For 9): Since \(11x + 10\) and \(12x\) are vertical angles (equal), we have the equation \(11x+10 = 12x\).

Subtract \(11x\) from both sides: \(10=12x - 11x\), so \(x = 10\).

• For 10): Since \(24x-4\) and \(23x + 2\) are vertical angles (equal), we have the equation \(24x-4=23x + 2\).

Subtract \(23x\) from both sides: \(24x-23x-4=2\), then \(x-4 = 2\). Add 4 to both sides: \(x=6\).

Answer:

1. Adjacent
2. Alternate exterior
3. Corresponding
4. Alternate interior
5. \(96^{\circ}\)
6. \(93^{\circ}\)
7. \(54^{\circ}\)
8. \(50^{\circ}\)
9. \(x = 10\)
10. \(x = 6\)