Answer:
ABC = 60
BCA = 90
CAB = 30
Step-by-step explanation:
5x+9x+6+90 = 180
5x+9x = 84
14x = 84
x = 6
5x = 30
9x+6 = 60
Given triangles are similar, so we setup a proportion
(140-x)/81 = x/9
solving gives x = 14
AC = 140-x = 140-14 = 126
There are many ways to do this. Such ways are using the quadratic formula, completing the square, etc.
We have
![x^2+10x-21=0](https://tex.z-dn.net/?f=x%5E2%2B10x-21%3D0)
We can add 46 to both sides so the -21 becomes a +25. by doing that, we get
![x^2+10x+25=46](https://tex.z-dn.net/?f=x%5E2%2B10x%2B25%3D46)
This can be wrote as
![(x+5)^2=46](https://tex.z-dn.net/?f=%28x%2B5%29%5E2%3D46)
We solve the square root and get
![(x+5)= +-\sqrt{46}](https://tex.z-dn.net/?f=%28x%2B5%29%3D%20%2B-%5Csqrt%7B46%7D%20)
(The +- is a plus minus sign.) Subtract five on both sides to get
![x=-5+- \sqrt{46}](https://tex.z-dn.net/?f=x%3D-5%2B-%20%5Csqrt%7B46%7D%20)
The answer is
C.