Question

question
∠1 and ∠2 are supplementary angles. if ( mangle1 = (x - 10)^circ ) and ( mangle2 = (8x + 28)^circ ), then find the measure of ( angle1 ).

Explanation:

Step1: Definir ángulos suplementarios

Ángulos suplementarios suman \( 180^\circ \). Entonces, \( m\angle1 + m\angle2 = 180^\circ \).
Sustituir \( m\angle1 = (x - 10)^\circ \) y \( m\angle2 = (8x + 28)^\circ \):
\( (x - 10) + (8x + 28) = 180 \)

Step2: Resolver para \( x \)

Combinar términos semejantes:
\( x + 8x - 10 + 28 = 180 \)
\( 9x + 18 = 180 \)
Restar 18 de ambos lados:
\( 9x = 180 - 18 \)
\( 9x = 162 \)
Dividir por 9:
\( x = \frac{162}{9} = 18 \)

Step3: Encontrar \( m\angle1 \)

Sustituir \( x = 18 \) en \( m\angle1 = (x - 10)^\circ \):
\( m\angle1 = (18 - 10)^\circ = 8^\circ \)

Answer:

\( 8^\circ \)