Question

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°

Explanation:

Step1: Recall parallel - line angle relationships

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

Step2: Analyze each option

• \(a = c\): \(a\) and \(c\) are vertical angles. Vertical angles are equal regardless of whether the lines are parallel or not, so this does not prove parallel lines.
• \(a = d\): \(a\) and \(d\) are corresponding angles. If corresponding angles are equal, then the two lines \(m\) and \(n\) are parallel.
• \(c = d\): \(c\) and \(d\) are alternate - interior angles. If alternate - interior angles are equal, then the two lines \(m\) and \(n\) are parallel.
• \(b + c=180^{\circ}\): \(b\) and \(c\) are adjacent angles. 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 two lines \(m\) and \(n\) are parallel.

Answer:

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