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 15° 15 degrees 105° 105 degrees 180°
Since angle B is adjacent to angles A and C, the sum of angles A, B, and C is equal to 180 degrees.
Given that angle C is 75 degrees, we can set up the equation:
A + B + C = 180.
Plugging in the value of angle C:
A + B + 75 = 180.
Subtracting 75 from both sides:
A + B = 105.
Since angles A and B share a vertex and add up to 105 degrees, each angle must be half of that amount:
m∠A = m∠B = 105/2 = 52.5 degrees.
Therefore, m∠A = 52.5°.