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 .

Answer 1

When two lines intersect, they create four angles that are classified as vertical angles and adjacent angles. Vertical angles are equal, while adjacent angles are supplementary (their measures add up to 180 degrees).

In this case, we have:

• Angle \( A \) is adjacent to angle \( B \)
• Angle \( C \) is adjacent to angle \( D \)
• Angle \( C \) is given as \( 75^\circ \)

Since angles \( A \) and \( C \) are vertical angles, they are equal. Therefore:

\[ m<A = m<C = 75^\circ \]

Thus, \( m<A = 75^\circ \).