Question

1. m∠2 = 24°. find the measure of the supplement of ∠2.
2. the arm of a crossing gate moves 42° from a vertical position. how many more degrees does the arm have to move so that it is horizontal?

Explanation:

Step1: Recall supplement - angle formula

The sum of an angle and its supplement is 180°. Let the angle be $\angle2 = 24^{\circ}$, and its supplement $\angle x$ satisfies $\angle2+\angle x = 180^{\circ}$.

Step2: Calculate the supplement of $\angle2$

$\angle x=180^{\circ}-\angle2 = 180 - 24=156^{\circ}$.

Step3: Recall supplement - angle formula for the second - level supplement

Let the supplement of $\angle x$ be $\angle y$. Then $\angle x+\angle y = 180^{\circ}$.

Step4: Calculate the supplement of the supplement of $\angle2$

$\angle y = 180^{\circ}-\angle x=180 - 156 = 24^{\circ}$.

Step5: Analyze the second problem

The vertical and horizontal directions are perpendicular, so the angle between them is 90°. The gate - arm has moved 42° from the vertical position. Let the additional angle it needs to move be $\theta$.

Step6: Calculate the additional angle

We know that $\theta=90^{\circ}-42^{\circ}=48^{\circ}$.

Answer:

1. $24^{\circ}$
2. $48^{\circ}$