When two lines intersect, adjacent angles are supplementary. So if one angle is $68^{\circ }$, the obtuse angle next to it is $180-68=112^{\circ }$. The third path is perpendicular to one of the original paths, so it makes a $90^{\circ }$ angle with that path. Since this third path lies inside the $112^{\circ }$ angle, it splits that angle into two parts: $90^{\circ }$ and the angle we want. Therefore, the unknown angle is $112-90=22^{\circ }$. The correct answer is $22^{\circ }$.

When two straight paths intersect, adjacent angles form a linear pair, so their measures add to $180^{\circ }$. Therefore, the angle adjacent to $58^{\circ }$ has measure $180-58=122$. The sign should show $122^{\circ }$.

Because the two streets are parallel and the road is a transversal, the angle in the upper-right position at one intersection and the angle in the lower-left position at the other intersection are alternate exterior angles. Alternate exterior angles are congruent, so
$3x+12=5x-24$.
Now solve:
$12=2x-24$
$36=2x$
$x=18$.
So the correct answer is $18$.

Adjacent angles formed by two intersecting straight roads make a linear pair, so their measures add to $180$. Let the smaller angle be $x$. Then the adjacent angle is described as $2x-18$. Set up the equation:

Combine like terms:

Add $18$ to both sides:

Divide by $3$:

So, the smaller adjacent angle measures $66$ degrees.

Adjacent angles formed by two intersecting lines are supplementary, so their measures add to $180$. Let the smaller angle be $x$. Then the adjacent angle is $2x+18$. Set up the equation: $x+(2x+18)=180$. Simplify: $3x+18=180$, so $3x=162$ and $x=54$. Therefore, the smaller adjacent angle measures $54$ degrees.