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

180°
180 degrees

105°
105 degrees

75°

1 answer

Since Angle C is 75°, Angle A and Angle B are supplementary angles. So, m∠A + m∠B = 180°. Therefore, m∠A = 180° - m∠B.
Since Angle B is adjacent to both Angle A and Angle C, it is also supplementary to Angle C. So, m∠B + m∠C = 180°. Therefore, m∠B = 180° - m∠C.
Substituting the value of m∠C = 75° into the equation, we get:
m∠B = 180° - 75°
m∠B = 105°

Now, substituting the value of m∠B = 105° into the equation m∠A = 180° - m∠B, we get:
m∠A = 180° - 105°
m∠A = 75°.

Therefore, m∠A = 75°.