Question

1. if the measure of an angle is $37\frac{1}{2}^{\circ}$, what is the measure of its supplement, shown in the figure below?

a. $52\frac{1}{2}^{\circ}$
b. $62\frac{1}{2}^{\circ}$
c. $127\frac{1}{2}^{\circ}$
d. $142\frac{1}{2}^{\circ}$
e. cannot be determined from the given information

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\). Let the given angle be \(A = 37\frac{1}{2}^{\circ}\) and its supplement be \(S\). Then the formula is \(A+S = 180^{\circ}\).

Step2: Solve for the supplement \(S\)

We can rewrite the formula as \(S=180^{\circ}-A\). Substitute \(A = 37\frac{1}{2}^{\circ}\) into the formula.
\(S = 180^{\circ}-37\frac{1}{2}^{\circ}\)
Convert \(180^{\circ}\) to \(179\frac{2}{2}^{\circ}\). Then \(S=179\frac{2}{2}^{\circ}-37\frac{1}{2}^{\circ}\)
Using the rule for subtracting mixed - numbers \((a\frac{b}{c}-d\frac{e}{c})=(a - d)\frac{b - e}{c}\), we have \(S=(179 - 37)\frac{2-1}{2}^{\circ}\)
\(S = 142\frac{1}{2}^{\circ}\)

Answer:

D. \(142\frac{1}{2}^{\circ}\)