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
180°
180 degrees
15°
15 degrees
105°
To find the measure of angle A, we need to use the fact that the sum of the angles at a vertex is always 180 degrees. Since angles B and C are adjacent to angle A, we have:
m∠A + m∠B + m∠C = 180
We know that m∠C = 75 degrees, so we can substitute this value into the equation:
m∠A + m∠B + 75 = 180
Simplifying the equation, we subtract 75 from both sides:
m∠A + m∠B = 105
Since angles B and A are adjacent, their measures add up to 105 degrees. We can then rearrange the equation to solve for m∠A:
m∠A = 105 - m∠B
We don't have any information about angle B, so we can't determine its measure. Therefore, we cannot determine the exact measure of angle A with the given information. The correct answer is "105°".