Vertical angles are angles opposite each other formed by two intersecting lines. These angles are always equal. Given this, we know the two angles are equal, i.e.,
[tex]\[ 170^\circ = (6k + 44)^\circ \][/tex]
To determine the value of [tex]\( k \)[/tex] that satisfies this equation, follow these steps:
1. Set up the equation:
[tex]\[ 170 = 6k + 44 \][/tex]
2. Isolate the variable [tex]\( k \)[/tex]:
[tex]\[ 170 - 44 = 6k \][/tex]
3. Simplify the left side:
[tex]\[ 126 = 6k \][/tex]
4. Solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{126}{6} \][/tex]
5. Calculate the value of [tex]\( k \)[/tex]:
[tex]\[ k = 21 \][/tex]
Therefore, the value of [tex]\( k \)[/tex] that satisfies the angle equation is
[tex]\[ k = 21 \][/tex]
