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
Since Angle B is adjacent to both Angle A and Angle C, and Angle C is given as 75°, we know that m∠B = 180° - m∠C (since the sum of angles in a straight line is 180°). Thus, m∠B = 180° - 75° = 105°.
Since all four angles have the same vertex, the sum of the measures of all four angles must be 360°. Therefore, m∠A + m∠B + m∠C + m∠D = 360°.
Substituting the given values, we have:
m∠A + 105° + 75° + m∠D = 360°
Simplifying the equation, we have:
m∠A + 180° + m∠D = 360°
m∠A + m∠D = 360° - 180°
m∠A + m∠D = 180°
We don't have any further information about Angle D, so we cannot determine its measure. Therefore, we cannot determine the exact measure of Angle A.