When two lines intersect, vertical angles are equal and adjacent angles are supplementary. Since one angle is $68^{\circ }$, each angle next to it must be $180^{\circ }-68^{\circ }=112^{\circ }$. Therefore, both adjacent angles measure $112^{\circ }$, so the statement that must be true is choice B.

The wall and floor form a right angle, so they make $90^{\circ }$. The beam forms a $68^{\circ }$ angle with the floor, so the angle between the beam and the wall is the rest of the right angle: $90-68=22$. Therefore, the correct answer is $22^{\circ }$.

The wall and ground form a right angle, so the ladder creates a right triangle. The two acute angles in a right triangle add to $90^{\circ }$. Therefore,

Combine like terms:

Subtract 15 from both sides:

Divide by 5:

So the correct answer is $15$.

When two lines intersect, any two adjacent angles form a linear pair. Linear pairs are supplementary, so their measures add to $180^{\circ }$. If one angle measures $x^{\circ }$, then an adjacent angle measures $180-x$ degrees. Therefore, the correct expression is $180-x$.

First find the slope of line $m$ using the two given points:

For a line that makes an angle $\theta$ with the positive $x$-axis, the slope is $\tan \theta$. So $\tan \theta =1$. The acute angle whose tangent is 1 is $45^{\circ }$. Therefore, the correct answer is $45^{\circ }$.