Two intersecting lines create four angles with the same vertex, labeled A , B , C , and D . Angle B is adjacent to ∠A and ∠C. Find m∠A if m∠C=75°

Question

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Answer 1

When two lines intersect, they create two pairs of vertically opposite angles. The angles are often labeled as follows:

• ∠A and ∠C are vertically opposite angles.
• ∠B and ∠D are vertically opposite angles.

Since vertically opposite angles are equal, we have:

\[ m∠A = m∠C \]

Given that \( m∠C = 75° \), we can find \( m∠A \):

[ m∠A = m∠C = 75° \