Angles Review — Answers

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1. Angle Foundations:

   1. x = 117° ▶ View Solution
   2. x = 125° ▶ View Solution
   3. 78° with parallel lines: Four angles of 78° and four angles of 102° ▶ View Solution
   4. Transversal at 90°: All 8 angles are 90° ▶ View Solution
   5. Vertically opposite supplementary: False — vertically opposite angles are equal, not supplementary (unless both are 90°) ▶ View Solution

2. Corresponding and Alternate Angles:

   1. Corresponding to 83°: 83° ▶ View Solution
   2. Alternate to 119°: 119° ▶ View Solution
   3. Corresponding to 47°: 47° ▶ View Solution
   4. Alternate to 63°: 63° ▶ View Solution
   5. Letter shapes: Corresponding → F-shape; Alternate → Z-shape ▶ View Solution
   6. Same side or opposite: Same side of the transversal ▶ View Solution

3. Co-interior Angles:

   1. 112° ▶ View Solution
   2. 65° ▶ View Solution
   3. 90° ▶ View Solution
   4. Co-interior always equal: False — they add to 180° ▶ View Solution
   5. Letter shape: C-shape (or U-shape) ▶ View Solution

4. Identify and Calculate:

   1. Same corner: Corresponding; x = 56° ▶ View Solution
   2. Same side between lines: Co-interior; x = 180 − 74 = 106° ▶ View Solution
   3. Opposite sides between lines: Alternate; x = 101° ▶ View Solution
   4. (4x + 5) + 79 = 180: 4x + 84 = 180; 4x = 96; x = 24 ▶ View Solution
   5. (2x − 8) = 64: 2x = 72; x = 36 ▶ View Solution
   6. (3x + 15) = 90: 3x = 75; x = 25 ▶ View Solution

5. Reasoning and Real-World Problems:

   1. Co-interior 88° and 87°: 88 + 87 = 175° ≠ 180°, so the lines are NOT parallel. ▶ View Solution
   2. Alternate 53° and 53°: Yes, the lines are parallel — equal alternate angles confirm parallel lines. ▶ View Solution
   3. 180° − 58° = 122° ▶ View Solution
   4. Post at 72°, corresponding and co-interior: Corresponding: 72°; co-interior: 180° − 72° = 108° ▶ View Solution
   5. (6x − 10) + (2x + 30) = 180: 8x + 20 = 180; 8x = 160; x = 20; angle A = 6(20)−10 = 110°; angle B = 2(20)+30 = 70°. Check: 110 + 70 = 180° ✓ ▶ View Solution

6. Angle Relationships Summary:

   1. Table: Corresponding: F-shape, Equal | Alternate: Z-shape, Equal | Co-interior: C-shape, Sum to 180° ▶ View Solution
   2. How to determine parallel lines: Measure angles: if corresponding or alternate pairs are equal, or if co-interior pairs sum to 180°, then the lines are parallel. ▶ View Solution