How will I start this problem? How will I get to my solution.

Question

After a sequence of rigid motions, the image of Triangle CAT is Triangle C’A’T’. If m<T= 3(x+2) and m<T’=x(x-2), determine and state the measure of <T. Only algebraic solution accepted.

Answer 1

After a sequence of rigid motions, all the ratios will still be the same. This means that m<T and m<T' are equal. So we have:

3(x+2)=x(x-2)

3x+6=x²-2x

x²-5x-6=0

(x-6)(x+1)=0

x=6,-1

m<T=3(6+2)=3(8)=24

m<T=3(-1+2)=3(1)=3

Both of these solutions work because both are greater than 0 but less than 180. However, m<T=24 is much more common than m<T=3.

Answer 2

3(x+2) = x(x-2)

3x + 6 = x^2 - 2x

0 = x^2 - 2x - 3x - 6

0 = x^2 - 5x - 6

( x - 6 )( x + 1 ) = 0

x=6 or x=-1, which results in negative measures

3(6+2) =3(8) = 24 = 6*4 = 6*(6-2)

24 degrees

Answer 3

3(x + 2) = x(x - 2)

Good start?