SOLUTION: Find the values of the variables: one angle = 90 degrees one angle = (2x-11) one angle = (y+16) two congruent sides are of the right angle (2x-11)+(y+16) = 90

Algebra ->  Triangles -> SOLUTION: Find the values of the variables: one angle = 90 degrees one angle = (2x-11) one angle = (y+16) two congruent sides are of the right angle (2x-11)+(y+16) = 90      Log On


   

Question 167677: Find the values of the variables:
one angle = 90 degrees
one angle = (2x-11)
one angle = (y+16)
two congruent sides are of the right angle
(2x-11)+(y+16) = 90
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Find the values of the variables:
one angle = 90 degrees
one angle = (2x-11)
one angle = (y+16)
.
Since you have two unknowns (x and y), you'll need two equations.
.
equation 1: (as you say)
(2x-11)+(y+16) = 90
.
since there are two congruent sides:
equation 2:
(2x-11)=(y+16)
.
Solve equation 2 for x:
(2x-11)=(y+16)
2x-11 = y+16
2x = y+27
x = (1/2)(y+27)
.
Plug the above into equation 1 and solve for y:
(2x-11)+(y+16) = 90
(2(1/2)(y+27)-11)+(y+16) = 90
y+27-11+y+16 = 90
2y+27-11+16 = 90
2y+16+16 = 90
2y+32 = 90
2y = 58
y = 29
.
Plug it back into equation 2 to find x:
(2x-11)=(y+16)
(2x-11)=(29+16)
2x-11=45
2x=56
x = 28
.
solution:
x is 28
y is 29