Question

find the complementary angle of \\(38\frac{1}{2}^{\circ}\\).

the complementary angle of \\(38\frac{1}{2}^{\circ}\\) is \\(\square^{\circ}\\).
(simplify your answer. type an integer, fraction, or mixed number.)

Explanation:

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<reasoning>

Define complementary angles

Using the Complementary Angles knowledge point
\[
\theta_1 + \theta_2 = 90^\circ
\]

Set up the equation

Using the Complementary Angles knowledge point
\[
38\frac{1}{2}^\circ + x = 90^\circ
\]

Solve for the unknown angle

Using the Complementary Angles knowledge point
\[

$$\begin{aligned} x &= 90 - 38\frac{1}{2} \\ x &= 89\frac{2}{2} - 38\frac{1}{2} \\ x &= 51\frac{1}{2} \end{aligned}$$

\]
</reasoning>

<answer>
The complementary angle of \(38\frac{1}{2}^\circ\) is <blank>\(51\frac{1}{2}\)</blank>\(^\circ\).
</answer>

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Answer:

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<reasoning>

Define complementary angles

Using the Complementary Angles knowledge point
\[
\theta_1 + \theta_2 = 90^\circ
\]

Set up the equation

Using the Complementary Angles knowledge point
\[
38\frac{1}{2}^\circ + x = 90^\circ
\]

Solve for the unknown angle

Using the Complementary Angles knowledge point
\[

$$\begin{aligned} x &= 90 - 38\frac{1}{2} \\ x &= 89\frac{2}{2} - 38\frac{1}{2} \\ x &= 51\frac{1}{2} \end{aligned}$$

\]
</reasoning>

<answer>
The complementary angle of \(38\frac{1}{2}^\circ\) is <blank>\(51\frac{1}{2}\)</blank>\(^\circ\).
</answer>

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