Questions: Dada la figura de abajo, halle los valores de x y z. x= z=

Dada la figura de abajo, halle los valores de x y z. x= z=
Transcript text: Dada la figura de abajo, halle los valores de $x y z$. \[ \begin{array}{l} x= \\ z= \end{array} \]
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Solution

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Paso 1: Identificar ángulos verticales

Los ángulos (10x - 54)° y (6x - 6)° son ángulos verticales, por lo que son congruentes.

Paso 2: Establecer la ecuación

Dado que los ángulos verticales son congruentes, podemos establecer la siguiente ecuación:

10x - 54 = 6x - 6

Paso 3: Resolver para x

Para resolver x, primero resta 6x de ambos lados de la ecuación:

4x - 54 = -6

Luego, suma 54 a ambos lados:

4x = 48

Finalmente, divide ambos lados por 4:

x = 12

Paso 4: Encontrar el valor de z

Los ángulos (10x - 54)° y z° son ángulos suplementarios, lo que significa que su suma es igual a 180°. Sustituimos el valor de x = 12 en la expresión (10x - 54)°:

10(12) - 54 = 120 - 54 = 66°

Entonces, podemos establecer la siguiente ecuación:

z + 66 = 180

Restando 66 de ambos lados, obtenemos:

z = 114

Respuesta final

\\(\boxed{x = 12}\\) \\(\boxed{z = 114}\\)

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