L60 — Co-interior Angles and Problem Solving — Solutions

1. Co-interior Angles

   1. 120° ▶ View Solution
   2. 70° ▶ View Solution
   3. 135° ▶ View Solution
   4. 45° ▶ View Solution

2. Mixed Angle Rules

   1. Same corner: Corresponding; x = 84° ▶ View Solution
   2. Same side between lines: Co-interior; x = 123° ▶ View Solution
   3. Z-shape: Alternate; x = 116° ▶ View Solution
   4. C-shape: Co-interior; x = 48° ▶ View Solution

3. Spot the Error

   1. Error about co-interior being equal: Co-interior angles add to 180° (supplementary), not equal ▶ View Solution
   2. Alternate adding to 180°: Incorrect — alternate angles are EQUAL, not supplementary; student confused alternate with co-interior ▶ View Solution
   3. Misunderstanding co-interior: Incorrect — co-interior angles add to 180°; 70 + 110 = 180° confirms they ARE co-interior of parallel lines ▶ View Solution
   4. Difference between co-interior and alternate: Alternate: opposite sides of transversal, equal; co-interior: same side, add to 180° ▶ View Solution

4. Complex Problems

   1. x = 37; angles 99° and 81° ▶ View Solution
   2. Co-interior at 47°: Co-interior = 133°; alternate = 47° — consistent ▶ View Solution
   3. Co-interior 95° and 80°: No — 95 + 80 = 175° ≠ 180°; lines NOT parallel ▶ View Solution
   4. Parallelogram with 65°: Adjacent = 115°; all four angles: 65°, 115°, 65°, 115° ▶ View Solution

5. Equations with Co-interior Angles

   1. x = 25; angles 110° and 70° ▶ View Solution
   2. x = 95÷6; angles ≈64.2° and 115.8° ▶ View Solution
   3. x = 25; angles 75° and 105° ▶ View Solution
   4. 10x + (8x + 4) = 180: x ≈9.78; angles ≈97.8° and 82.2° ▶ View Solution

6. Choose the Right Rule

   1. x = 8; each angle = 29° (alternate angles equal) ▶ View Solution
   2. x = 20; each angle = 70° (corresponding angles equal) ▶ View Solution
   3. x = 30; angles 100° and 80° (co-interior sum to 180°) ▶ View Solution
   4. Co-interior pair 65° and 115°, plus vertically opposite: Upper: 65°, 115°, 65°, 115°  |  Lower: 115°, 65°, 115°, 65° ▶ View Solution

7. Are the Lines Parallel?

   1. 85 + 95 = 180: Yes — co-interior angles sum to 180°; lines are parallel ▶ View Solution
   2. 100 + 75 = 175 ≠ 180: No — 175° ≠ 180°; lines not parallel ▶ View Solution
   3. x = 30; angles 100° and 80°; lines parallel when x = 30 ▶ View Solution
   4. 89.5 + 91 = 180.5 ≠ 180: No — sum is 180.5°, not exactly 180° ▶ View Solution

8. Combining All Three Rules

   1. b = 65°, c = 65°, d = 115° (upper intersection)  |  e = 115°, f = 65°, g = 65°, h = 115° (lower intersection) ▶ View Solution
   2. Triangle between the transversals: 60° (triangle angle sum: 180 − 70 − 50, using alternate angles at the transversal intersections) ▶ View Solution
   3. Parallelogram with 72°: Adjacent = 108°; all four: 72°, 108°, 72°, 108° ▶ View Solution

9. Real-world Context

   1. Ladder at 72° co-interior: 108° ▶ View Solution
   2. x = 16; angles 104° and 76° ▶ View Solution
   3. Grout at 112° co-interior: Same side at second row: 68° (co-interior)  |  Opposite side: 112° (alternate) ▶ View Solution

10. Investigation — All Angle Rules

    1. p = 58°: Equal to 58°: p, vertically opposite at upper, corresponding at lower, alternate at lower. Equal to 122°: the other four angles ▶ View Solution
    2. x = 32 (co-interior at upper + corresponding angle at lower = 180; 4x + 52 = 180) ▶ View Solution
    3. Rules break down for non-parallel lines: Rules only hold for parallel lines — non-parallel lines give unequal corresponding/alternate angles and co-interior sum ≠ 180° ▶ View Solution