Question 907744
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.