Question

find the supplementary angle of \\(23\frac{3}{5}^{\circ}\\).

the supplementary angle of \\(23\frac{3}{5}^{\circ}\\) is \\(\box^{\circ}\\).
(simplify your answer. type an integer, fraction, or mixed number.)

Explanation:

Define supplementary angles

Two angles are supplementary if their sum is exactly \(180^\circ\). Using the Supplementary Angles concept, if we have a given angle \(\theta\), its supplementary angle \(S\) is calculated by subtracting \(\theta\) from \(180^\circ\):

$$S = 180^\circ - \theta$$

Set up the subtraction

The given angle is \(\theta = 23\frac{3}{5}^\circ\). We need to find:

$$S = 180 - 23\frac{3}{5}$$

Perform the calculation

To subtract the mixed number from the integer, we can rewrite \(180\) as \(179\frac{5}{5}\):

$$S = 179\frac{5}{5} - 23\frac{3}{5}$$

Subtract the whole numbers and the fractions separately:

$$179 - 23 = 156$$

$$\frac{5}{5} - \frac{3}{5} = \frac{2}{5}$$

Combining these gives:

$$S = 156\frac{2}{5}$$

Answer:

The supplementary angle of \(23\frac{3}{5}^\circ\) is <blank>\(156\frac{2}{5}\)</blank>\(^\circ\).