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
15°
15 degrees
180°
We know that angle B is adjacent to angles A and C, meaning that angle A and angle C share a side with angle B. Since the sum of the angles in a triangle is 180 degrees, we can determine that angle B + angle A + angle C = 180.
Since we are given that angle C = 75 degrees, we can substitute this value into the equation.
angle B + angle A + 75 = 180
We can subtract 75 from both sides to isolate angle B and angle A.
angle B + angle A = 105
Since angle B and angle A share a side with angle C, we can conclude that they must be equal. So angle B = angle A.
Substituting angle A with angle B, we get:
2angle B = 105
Dividing both sides by 2, we find that angle B = 52.5 degrees.
Since angle A is equal to angle B, angle A also equals 52.5 degrees.