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:

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<reasoning>

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:
\[S = 156\frac{2}{5}\]
</reasoning>

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

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Answer:

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<reasoning>

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:
\[S = 156\frac{2}{5}\]
</reasoning>

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

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