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 15° 15 degrees 105° 105 degrees 180° 180 degrees 75°
Since angle B is adjacent to angle A and angle C, it is an interior angle formed by the two intersecting lines. Thus, m∠B + m∠C = 180°. If m∠C = 75°, then m∠B + 75° = 180°. Solving for m∠B, we subtract 75° from both sides to get m∠B = 105°. Since angle A and angle B are adjacent, they are supplementary angles. Thus, m∠A + m∠B = 180°. Substituting m∠B = 105°, we have m∠A + 105° = 180°. Solving for m∠A, we subtract 105° from both sides to get m∠A = 75°. Therefore, the answer is 75°.
