Question

the angles shown are complementary angles. determine the measures of \\(\angle 1\\) and \\(\angle 2\\).

what are the measures of \\(\angle 1\\) and \\(\angle 2\\)?

\\(m\angle 1 = \square^{\circ}\\) (simplify your answer.)
\\(m\angle 2 = \square^{\circ}\\) (simplify your answer.)

Explanation:

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<reasoning>

Set up the angle equation

Using the Complementary Angles knowledge point, we know that complementary angles sum to \(90^\circ\).
\[
\mathrm{m}\angle 1 + \mathrm{m}\angle 2 = 90^\circ
\]

Substitute the given expressions

We substitute the given algebraic expressions for each angle into the equation.
\[
(19x + 10) + x = 90
\]

Solve for x

We combine like terms and solve the linear equation.
\[

$$\begin{aligned} 20x + 10 &= 90 \\ 20x &= 80 \\ x &= 4 \end{aligned}$$

\]

Calculate the angle measures

We substitute \(x = 4\) back into the expressions for each angle.
\[

$$\begin{aligned} \mathrm{m}\angle 1 &= 19(4) + 10 = 76 + 10 = 86^\circ \\ \mathrm{m}\angle 2 &= 4^\circ \end{aligned}$$

\]
</reasoning>

<answer>
What are the measures of \(\angle 1\) and \(\angle 2\)?

\(\mathrm{m}\angle 1 =\) <blank>86</blank>\(^\circ\)
\(\mathrm{m}\angle 2 =\) <blank>4</blank>\(^\circ\)
</answer>

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Answer:

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<reasoning>

Set up the angle equation

Using the Complementary Angles knowledge point, we know that complementary angles sum to \(90^\circ\).
\[
\mathrm{m}\angle 1 + \mathrm{m}\angle 2 = 90^\circ
\]

Substitute the given expressions

We substitute the given algebraic expressions for each angle into the equation.
\[
(19x + 10) + x = 90
\]

Solve for x

We combine like terms and solve the linear equation.
\[

$$\begin{aligned} 20x + 10 &= 90 \\ 20x &= 80 \\ x &= 4 \end{aligned}$$

\]

Calculate the angle measures

We substitute \(x = 4\) back into the expressions for each angle.
\[

$$\begin{aligned} \mathrm{m}\angle 1 &= 19(4) + 10 = 76 + 10 = 86^\circ \\ \mathrm{m}\angle 2 &= 4^\circ \end{aligned}$$

\]
</reasoning>

<answer>
What are the measures of \(\angle 1\) and \(\angle 2\)?

\(\mathrm{m}\angle 1 =\) <blank>86</blank>\(^\circ\)
\(\mathrm{m}\angle 2 =\) <blank>4</blank>\(^\circ\)
</answer>

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