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 angle B is adjacent to angles A and C, it means that angle B is formed by the two intersecting lines.

Since angles A, B, C, and D are total 360 degrees in a full rotation, we can say that angle B + angle D = 360 degrees.

Since angle C is given as 75 degrees, it means angle D is equal to 360 degrees – angle C = 360 degrees – 75 degrees = 285 degrees.

Since angles A, B, C, and D are formed by intersecting lines, we can say that angle A + angle B = 180 degrees.

Since angle B is equal to the sum of angles A and C, we have angle B = angle A + angle C.

Substituting the values, we can say: angle A + (angle A + 75 degrees) = 180 degrees.

Combining like terms, we have 2 * angle A + 75 degrees = 180 degrees.

Subtracting 75 degrees from both sides, we get 2 * angle A = 180 degrees – 75 degrees = 105 degrees.

Dividing both sides by 2, we have angle A = 105 degrees / 2 = <<105/2=52.5>>52.5 degrees.

Therefore, m∠A = 52.5 degrees. Answer: \boxed{52.5}.