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Question 890297: The difference if the measures of angle A and angle B is 80, where the measure of angle A is greater than that of angle B. 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. What are the measures of angle A and angle B?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
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