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
75°
75 degrees
105°
105 degrees
180°
180 degrees
15°
To find the measure of angle A, we need to use the property of straight lines.
Since angles A and C are adjacent and lie on a straight line, they are supplementary angles. This means that the sum of their measures is 180 degrees.
Given that angle C is 75 degrees, we can set up the equation:
m∠A + 75° = 180°
Subtracting 75 degrees from both sides, we have:
m∠A = 180° - 75° = 105°
Therefore, the measure of angle A is 105 degrees.