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
75°
75 degrees
105°
To find the measure of angle A, we can use the fact that angles around a vertex add up to 360 degrees. Since angles B and C are adjacent to angle A, we can write the equation:
angle A + angle B + angle C = 360
Substituting in the value for angle C (75 degrees), we have:
angle A + angle B + 75 = 360
Since angle B is adjacent to angle A and C, we know that it is also 75 degrees:
angle A + 75 + 75 = 360
Combining like terms:
angle A + 150 = 360
Subtracting 150 from both sides:
angle A = 210
Therefore, the measure of angle A is 210 degrees.