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° .(1 point) Responses 105° 105 degrees 180° 180 degrees 15° 15 degrees 75°

Answer 1

In the situation described, since angles \( A \), \( B \), \( C \), and \( D \) are formed by two intersecting lines, we note that:

1. \( \angle A \) and \( \angle C \) are opposite angles, and thus they are equal: \[ m\angle A = m\angle C. \]

2. \( \angle A \) and \( \angle B \) are adjacent angles, which means they add up to \( 180^\circ \): \[ m\angle A + m\angle B = 180^\circ. \]

Since we know that \( m\angle C = 75^\circ \): \[ m\angle A = m\angle C = 75^\circ. \]

Thus, the correct answer for \( m\angle A \) is \( 75^\circ \).

To confirm:

• \( m\angle B = 180^\circ - m\angle A = 180^\circ - 75^\circ = 105^\circ \).
• \( m\angle D \) would also equal \( m\angle B = 105^\circ \).

So, the final answer is:

75°.