Question

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)
A• 105°
B• 15°
C• 180°
D• 75°

Answer 1

Since angle C is 75° and angles B and C are adjacent, we know that angle B is also 75°. And because angles A, B, C, and D all share the same vertex, the sum of their measures must equal 360°.

So, if we let m A be the measure of angle A, we have:

m A + m B + m C + m D = 360°

Substituting in the known values:

m A + 75° + 75° + m D = 360°

Simplifying:

m A + m D = 360° - 150°

m A + m D = 210°

Since we do not have any specific information about angle D, we cannot determine its measure. Therefore, we cannot determine the exact measure of angle A.

The correct answer choice is: Cannot be determined.