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.
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
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