SOLUTION: 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 compleme

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

RELATED QUESTIONS
angle a and angle b are supplementary angles. find the measures of each angle if angle is (answered by ikleyn)

In triangle A,B,C the measure of B is twice the measure of angle A the measure of angle C (answered by jorel1380)

Angle A and angle B are complementary angles.If angle A measures 49 degrees,what is the... (answered by ewatrrr)

angles a and angle b are supplementary angles find the measure of each angle if angle a... (answered by Stitch)

Two angles are complementary if the sum of their measures is 90 degress. If angle A and B (answered by nerdybill)

If an angle Measures 48 less than the measure of a complementary angle where is the... (answered by josgarithmetic,MathTherapy)

recall that the measures of a triangle is 180 degrees. In a triangle angle C has the same (answered by rfer)

Angle A and angle B are supplementary angles and angle A is 30 less than four times angle (answered by Alan3354)

Angle A and angle B are supplementary angles and angle A is 35° less than four times... (answered by greenestamps)