Question

the following is an isometry. find the value of each variable. lo siguiente es una isometría. encuentra el valor de cada variable. x = type your answer... y = type your answer... z = type your answer... (13y + 4)° 108° 5x 3x+22 40° (7z - 2)°

Explanation:

Step1: Equate corresponding - side lengths

Since it is an isometry, corresponding side - lengths are equal. We set up the equation for the side - lengths: $5x=3x + 22$.
Subtract $3x$ from both sides: $5x-3x=3x + 22-3x$, which simplifies to $2x=22$.
Divide both sides by 2: $x=\frac{22}{2}=11$.

Step2: Equate corresponding angles

Corresponding angles are equal. We set up the equation for the angles: $13y + 4=108$.
Subtract 4 from both sides: $13y+4 - 4=108 - 4$, which gives $13y=104$.
Divide both sides by 13: $y=\frac{104}{13}=8$.

Step3: Equate another pair of corresponding angles

Set up the equation for the angles: $7z-2 = 40$.
Add 2 to both sides: $7z-2 + 2=40 + 2$, which gives $7z=42$.
Divide both sides by 7: $z=\frac{42}{7}=6$.

Answer:

$x = 11$
$y = 8$
$z = 6$