Final answer:
To find the measure of the supplement of angle A, first find the measure of angle A by setting up an equation with the given information. Then, subtract the measure of angle A from 180 to find the measure of its supplement.
Step-by-step explanation:
To find the measure of the supplement of angle A, we first need to find the measure of angle A. It is given that angles A and B are complements, which means that their measures add up to 90 degrees. Let's represent the measure of angle B as x. According to the given information, the measure of angle A is 6 less than 7 times the measure of angle B, so the measure of angle A is 7x - 6. We can set up the equation 7x - 6 + x = 90, since the measures of angles A and B add up to 90 degrees. Solving this equation, we find that x = 12. Now we can find the measure of angle A by substituting x = 12, which gives us A = 7(12) - 6 = 78.
The supplement of an angle is the angle that, when added to the given angle, sums to 180 degrees. Therefore, to find the measure of the supplement of angle A, we subtract the measure of angle A from 180. Substituting A = 78, we get the measure of the supplement of angle A as S = 180 - 78 = 102 degrees.