L58 — Angles and Parallel Lines — Solutions

1. Angles on a Straight Line

   1. x = 115° ▶ View Solution
   2. x = 50° ▶ View Solution
   3. x = 132° ▶ View Solution
   4. x = 108° ▶ View Solution

2. Vertically Opposite Angles

   1. x = 40° ▶ View Solution
   2. x = 115° ▶ View Solution
   3. x = 62° ▶ View Solution
   4. x = 52° ▶ View Solution

3. Find x at an Intersection

   1. x = 106° (angles on a straight line: 180° − 74°) ▶ View Solution
   2. x = 125° (angles on a straight line: 180° − 55°) ▶ View Solution
   3. x = 92° (angles on a straight line: 180° − 88°) ▶ View Solution
   4. x = 44° (vertically opposite) ▶ View Solution

4. All Eight Angles

   1. 52°: four angles of 52° and four angles of 128° ▶ View Solution
   2. 118°: four angles of 118° and four angles of 62° ▶ View Solution
   3. 73°: four angles of 73° and four angles of 107° ▶ View Solution
   4. 90°: all eight angles = 90° ▶ View Solution

5. Algebra on a Straight Line

   1. x = 38; angles: 86° and 94° ▶ View Solution
   2. x = 30; angles: 90°, 30°, 60° ▶ View Solution
   3. x = 12; each angle = 52° ▶ View Solution
   4. x = 20; angles: 85° and 95° ▶ View Solution

6. Name the Angle Relationship

   1. Vertically opposite; x = 58° ▶ View Solution
   2. Supplementary (on a straight line); x = 143° ▶ View Solution
   3. Supplementary (adjacent at same intersection); x = 131° ▶ View Solution
   4. Vertically opposite; x = 121° ▶ View Solution

7. Are These Angle Values Possible?

   1. No — vertically opposite angles are equal, not different. The actual vertically opposite angle is also 95°. ▶ View Solution
   2. Yes — three angles of 60° each sum to 60 + 60 + 60 = 180°. ✓ Three angles can sit on a straight line as long as they add to 180°. ▶ View Solution
   3. Consistent: 70° + 110° = 180° (straight line) ✓; vertically opposite pairs: 70° = 70° and 110° = 110° ✓; total: 70 + 110 + 70 + 110 = 360° ✓ ▶ View Solution
   4. One distinct angle size — all 8 angles = 90°. When the transversal is perpendicular to the parallel lines, every angle at both intersections is a right angle. ▶ View Solution

8. Real-World Parallel Lines

   1. 52° and 128°; four of each across both beams ▶ View Solution
   2. 68° at first crossing (given); vertically opposite = 68°; straight line = 112°; vertically opposite = 112°; second crossing: identical — 68°, 68°, 112°, 112° ▶ View Solution

9. Algebra and Reasoning

   1. Four angles: x°, (180−x)°, x°, (180−x)°. Sum = 2x + 2(180−x) = 2x + 360 − 2x = 360° ✓ ▶ View Solution
   2. 3n + (180 − 3n) = 3n + 180 − 3n = 180° ✓ — the 3n terms cancel for any n ▶ View Solution
   3. 70 + 50 + x + 80 + y = 360; x + y = 160; x = y (vertically opposite); so x = y = 80° ▶ View Solution

10. Investigation

    1. 4 distinct sizes: 60°, 120°, 40°, 140° ▶ View Solution
    2. 80° (triangle: 180° − 60° − 40° = 80°) ▶ View Solution
    3. q = 180 − p − t (from triangle angle sum: p + q + t = 180) ▶ View Solution