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)
• 105°
• 15°
• 180°
• 75°
Since angle B is adjacent to both angles A and C, angle B must be the sum of angles A and C. If angle C is 75°, then angle B is also 75°.
Using the fact that the sum of the angles around a point is 360°, we can find angle A by subtracting the sum of angles B, C, and D from 360°.
Angle A = 360° - (angle B + angle C + angle D)
Angle A = 360° - (75° + 75° + 90°) = 360° - 240° = 120°
Therefore, m A = 120°.