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° .(
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Since angle B is adjacent to angle A and angle C, it means that angle B and angle C are supplementary (their measures add up to 180 degrees). Therefore, if the measure of angle C is 75 degrees, the measure of angle B is 180 degrees minus 75 degrees, which is 105 degrees. Since angle A and angle C share the same vertex, angle A would then be supplementary to angle B (their measures add up to 180 degrees). Therefore, angle A would be 180 degrees minus 105 degrees, which is 75 degrees.
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