Please help with math

Scale factor  = 3

Step-by-step explanation:

Using similar triangles

AT/AG = AB/AC

9/3 = x+10/3x-10

Cross multiply

3(x+10) = 9(3x-10)

Expand

3x+30 = 27x-90

3x-27x = -90 - 30

-24x = -120

x = 120/24

x = 5

For the larger triangle;

AC = 3x-10

AC = 3(5)-10

AC =15-10

AC = 5

AB = x+10

AB = 5+10

AB = 15

For the scale factor;

Since AT/AG = AB/AC

9/15 = 3/5

3*3/5*3 =3/5

Since the numerator and denominator of the larger triangle is multiplies by the same factor i.3 3. Hence the scale factor is 3

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)