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)

Question

Responses

15°
15 degrees

180°
180 degrees

75°
75 degrees

105°

Answer 1

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.