letters a, b, c, and d are angles measures. which equation is enough information to prove that lines m and n…

letters a, b, c, and d are angles measures. which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? select three options. a = c a = d c = d b + c = 180° b + d = 180°

letters a, b, c, and d are angles measures. which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? select three options. a = c a = d c = d b + c = 180° b + d = 180°

Answer

Explanation:

Step1: Recall parallel - line angle relationships

When two parallel lines (m) and (n) are cut by a transversal (p), alternate - interior angles are equal, corresponding angles are equal, and same - side interior angles are supplementary.

Step2: Analyze each option

  • (a = c): (a) and (c) are vertical angles. Vertical - angle equality does not prove parallel lines.
  • (a = d): (a) and (d) are corresponding angles. If corresponding angles are equal, then the lines (m) and (n) are parallel.
  • (c = d): (c) and (d) are alternate - interior angles. If alternate - interior angles are equal, then the lines (m) and (n) are parallel.
  • (b + c=180^{\circ}): (b) and (c) are adjacent angles, and their sum being (180^{\circ}) does not prove parallel lines.
  • (b + d = 180^{\circ}): (b) and (d) are same - side interior angles. If same - side interior angles are supplementary ((b + d=180^{\circ})), then the lines (m) and (n) are parallel.

Answer:

B. (a = d), C. (c = d), E. (b + d = 180^{\circ})