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)
Since ∠B is adjacent to ∠A and ∠C, we know that ∠B + ∠A + ∠C = 180° (the sum of angles in a triangle).
Plugging in ∠C = 75°, we have ∠B + ∠A + 75° = 180°.
Subtracting 75° from both sides, we get ∠B + ∠A = 105°.
Since ∠A and ∠B are adjacent angles, they form a linear pair, which means they add up to 180°.
So, ∠A + ∠B = 180°.
We can set up the following system of equations:
∠A + ∠B = 180°
∠A + ∠B = 105°
Subtracting the second equation from the first, we get:
0 = 75°
This is a contradiction, which means there is no value of ∠A that satisfies the given conditions.
Therefore, the answer is undefined or there is no solution.