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
180°
180 degrees
75°
75 degrees
15°
15 degrees
105°
Since ∠C is given as 75° and ∠A and ∠B are adjacent angles, they must add up to 180 degrees (as they form a straight line). Therefore, ∠A + ∠B = 180°.
Since ∠B is adjacent to both ∠A and ∠C, it is also equal to 75°.
Substituting this value into the equation ∠A + ∠B = 180°: ∠A + 75° = 180°
Subtracting 75° from both sides of the equation, we get:
∠A = 180° - 75°
∠A = 105°
Therefore, m∠A is equal to 105°.