Two interesting lines create four angles with the same vertex, labeled A, B, C, and D. Angle B is to <A and <C. Find m<A if m<C = 75.

1 answer

Since angle B shares a vertex with angles A and C, we can conclude that all three angles are adjacent angles. Therefore, the sum of the measures of angles A, B, and C must equal 180 degrees.

Knowing that angle C measures 75 degrees, we can substitute this value into the equation:

A + B + 75 = 180

To find the measure of angle A, we can isolate it by subtracting 75 and B from both sides of the equation:

A = 180 - 75 - B
A = 105 - B

Therefore, the measure of angle A is 105 - B.