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° .

Answer 1

Since angles B and C are adjacent, they form a linear pair. This means that the sum of their measures is 180 degrees.

Therefore, we can set up the equation:

m∠B + m∠C = 180

m∠B + 75 = 180

Subtracting 75 from both sides of the equation, we find that:

m∠B = 180 - 75 = 105

Since angles A and B are adjacent, they also form a linear pair. Therefore, the sum of their measures is 180 degrees.

Therefore, we can set up the equation:

m∠A + m∠B = 180

m∠A + 105 = 180

Subtracting 105 from both sides of the equation, we find that:

m∠A = 180 - 105 = 75

Therefore, the measure of angle A is 75 degrees.