Question

the angles shown are supplementary 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 Supplementary Angles knowledge point
\[
(13x + 12) + x = 180
\]

Solve for x

Using the Systems of Linear Equations knowledge point
\[

$$\begin{aligned} 14x + 12 &= 180 \\ 14x &= 168 \\ x &= 12 \end{aligned}$$

\]

Calculate the measure of angle 1

Using the Supplementary Angles knowledge point
\[
\text{m}\angle 1 = x = 12^\circ
\]

Calculate the measure of angle 2

Using the Supplementary Angles knowledge point
\[
\text{m}\angle 2 = 13(12) + 12 = 156 + 12 = 168^\circ
\]
</reasoning>

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

\(\text{m}\angle 1 =\) <blank>\(12\)</blank>\(^\circ\)
\(\text{m}\angle 2 =\) <blank>\(168\)</blank>\(^\circ\)
</answer>

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Answer:

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<reasoning>

Set up the angle equation

Using the Supplementary Angles knowledge point
\[
(13x + 12) + x = 180
\]

Solve for x

Using the Systems of Linear Equations knowledge point
\[

$$\begin{aligned} 14x + 12 &= 180 \\ 14x &= 168 \\ x &= 12 \end{aligned}$$

\]

Calculate the measure of angle 1

Using the Supplementary Angles knowledge point
\[
\text{m}\angle 1 = x = 12^\circ
\]

Calculate the measure of angle 2

Using the Supplementary Angles knowledge point
\[
\text{m}\angle 2 = 13(12) + 12 = 156 + 12 = 168^\circ
\]
</reasoning>

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

\(\text{m}\angle 1 =\) <blank>\(12\)</blank>\(^\circ\)
\(\text{m}\angle 2 =\) <blank>\(168\)</blank>\(^\circ\)
</answer>

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