Question 890297
the equations are shown below.


A > B


A - B = 80


complement of B is equal to (90 - B)


supplement of complement of B is equal to (180 - (90 - B))


supplement of A is equal to (180 - A)


the sum of the measures of the supplement of the complement of angle B and the supplement of angle A is forty more than three times the measure of the complement of angle B becomes:


(180 - (90 - B) + (180 - A) = 3 * (90 - B) + 40


simplify this formula to get:


180 - 90 + B + 180 - A = 270 - 3B + 40


simplify this to get:


270 + B - A = 310 - 3B


subtract 270 and subtract B from both sides of this equation to get;


-A = 40 - 4B


multiply both sides of this equation by -1 to get:


A = 4B - 40


you know that A - B = 80 which means that A = B + 80


Replace A in the equation of A = 4B - 40 to get:


B + 80 = 4B - 40


add 40 to both sides of this equation and subtract B from both sides of this equation to get:


120 = 3B


solve for B to get:


B = 40


since A = B + 80, then A = 120.


that should be your answer.


confirm by going back to the original equations to see if all the statments made there hold true.


A - B = 80 becomes 120 - 40 = 80 which becomes 80 = 80 so that statement is true.


A > B becomes 120 > 40 so that statement is true.


The sum of the measures of the supplement of the complement of angle B and the supplement of angle A is forty more than three times the measure of the complement of angle B leads to the formula shown below:


(180 - (90 - B) + (180 - A) = 3 * (90 - B) + 40


replace A with 120 and B with 40 in this equation to get:


(180 - (90 - 40) + (180 - 120) = 3 * (90 - 40) + 40


simplify this equation to get:


130 + 60 = 3 * (50) + 40


simplify further to get:


190 = 150 + 40


simplify further to get:


190 = 190 which is true, so the statement leading to this formula is true when A = 120 and B = 40.


looks like the solution is good.


A = 120
B = 40