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 75° 75 degrees 180° 180 degrees
We know that ∠A and ∠C are adjacent angles, which means they share a common side and vertex. Since they are adjacent, the sum of their measures is 180 degrees.
m∠A + m∠C = 180°
We are given that m∠C = 75°, so we can substitute that into the equation:
m∠A + 75° = 180°
To solve for m∠A, we can subtract 75° from both sides:
m∠A = 180° - 75°
m∠A = 105°
Therefore, the measure of ∠A is 105 degrees.