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

15°
15 degrees

105°
105 degrees

75°
The sum of the angles around a point is always 360 degrees. Since angle C is 75 degrees, angles A and B must add up to 360 - 75 = 285 degrees. Since angle B is adjacent to both angle A and C, angle B must be half of the sum of angles A and C.
Let x be the measure of angle A. Then angle B is (285 - x)/2.
We can set up an equation:
x + (285 - x)/2 = 75
Multiplying both sides by 2:
2x + 285 - x = 150
Simplifying:
x + 285 = 150
Subtracting 285 from both sides:
x = -135
However, since angles must be positive, this solution is extraneous.
Therefore, there is no valid solution for the measure of angle A given that angle C is 75 degrees.