Question

Two angles whose measures have a sum of 90° are called complementary angles. for exercises 28–30, x and y represent complementary angles. find the measure of each angle. 28.    x + y = 90 y = 4x - 10 29.    x = 2y x + y = 90 30.    y = 2 (x - 15) x + y = 90

Answer 1

28: x+y = 90
we substitute y with the given function 4x - 10
x + 4x - 10 = 905x -10 = 90 5x = 100= 100 ÷ 5x = 20, now you can substitute x in 4x - 10 =4(20) - 1080 - 10 = 70, which makes sense as 20º +70º = 90ºyour 2 angles are 20º and 70º
29:  x + y = 90  x = 2y
Same thing we did above, substitute the given variable into the given equation
so, 2y + y = 90 = 3y=90, divide the 3 to both sides, y = 30, now substitue the y into your given x variable.x = 2(30)x= 60this makes sense as 60º + 30º do equal 90ºyour two angles are 60º and 30º30:  x + y = 90 y = 2 (x - 15)ill do this one without explanation as you know what I am doing from the above examples. here is the work:
x + 2(x-15)=90 (simplify)
x+2x-30 = 903x-30=903x = 120x = 40now input to other equation2(40 - 15) = y (USE PEMDAS)2(25) = yy = 50
makes sense because 50º + 40º = 90ºyour two angles are 50º and 40º