Question

I need to know how the solve the answers below

Answer 1

S is given as 58 degrees.

There are 180 degrees in a triangle. Using this you know that S + T + TUS = 180

T is given as 5x + 10

TUS can be defined as TUS + AUT = 180, or TUS = 180 - AUT

AUT is given as 11x + 2

Plug everything into the first equation to give you 58 + (5x + 10) + (180 - (11x + 2)) = 180

Solve for x, and be careful with the negative in front of (11x+2)

58 + 10 + 180 - 2 + 5x - 11x = 180

-6x = -66
x = 11

Plug x back into the equations for AUT and T to get your final answers.

AUT = 11(11) + 2 = 123 degrees
S = 58 degrees
T = 5(11) + 10 = 65 degrees
TUS = 180 - AUT = 180 - 123 = 57 degrees

You can check your answer by making sure
S + T + TUS = 180, which it does.