SOLUTION: Angle A and Angle B form a linear pair. Fifty one less than the measure of angle B is equal to twice the measure of angle A. What is the measure OF THE COMPLEMENT OF ANGLE A?

Question 907744: Angle A and Angle B form a linear pair. Fifty one less than the measure of angle B is equal to twice the measure of angle A. What is the measure OF THE COMPLEMENT OF ANGLE A?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A and B form a linear pair.
this means A + B = 180

fifty one less than the measure of B is equal to 2 * the measure of A.
this means B - 51 = 2 * A

you want to find the complement of A.
this means you want to find 90 - A.

you have 2 equations that need to be solved simultaneously to get a solution that is common to both of them.

the equations are:

A + B = 180 (first equation)
B - 51 = 2 * A (second equation)

solve for A in the first equation to get A = 180 - B

replace A with 180 - B in the second equation to get B - 51 = = 2 * (180 - B)

this allows you to solve for B in the second equation.

simplify to get B - 51 = 2 * 180 - 2 * B

simplify further to get B - 51 = 360 - 2 * B

add 2 * B to both equations to get 3 * B - 51 = 360

add 51 to both sides of the equation to get 3 * B = 411

divide both sides of the equation by 3 to get B = 137

replace B in the first equation with 137 to get A + 137 = 180

subtract 137 from both sides of the equation to get A = 43

you want to find the complement of A so you want to find 90 - A.

replace A in that equation with 43 to get complement of A = 90 - 43 which makes the complement of A = 47 degrees.

that's your solution.

you can go back to your original equations to confirm the solution is correct.

if the complement of A is 47, this means that A is 43.

you already solved for B to get B = 137.

A + B = 180 becomes 43 + 137 = 180 which becomes 180 = 180.
this confirms that A and B are correct.

fifty one less than B is equal to twice A becomes 137 - 51 = 2*43 which becomes 86 = 86.
this confirms that fifty one less than B is equal to twice A.

the solution of A = 43 and B = 137 is correct.

the complement of A is equal to 9 - 43 which is equal to 47 which is the solution you were asked to find.

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