Question

the angles to the right are complementary angles. determine the measure of \\(\measuredangle 1\\) and \\(\measuredangle 2\\).

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

\\(m\measuredangle 1 = \boxed{\phantom{x}}^{\circ}\\) (simplify your answer.)
\\(m\measuredangle 2 = \boxed{\phantom{x}}^{\circ}\\) (simplify your answer.)

Explanation:

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<reasoning>

Set up the angle relationship

Using the Complementary Angles knowledge point, we know that two angles are complementary if the sum of their measures is exactly \(90^\circ\). From the given diagram, the measures of the two adjacent angles are:
\[m\angle 1 = 9x - 20\]
\[m\angle 2 = x\]
Since they are complementary, we write the equation:
\[(9x - 20) + x = 90\]

Solve for x

We combine the like terms and solve the linear equation:
\[10x - 20 = 90\]
\[10x = 110\]
\[x = 11\]

Calculate the measure of angle 1

We substitute \(x = 11\) back into the expression for \(m\angle 1\):
\[m\angle 1 = 9(11) - 20\]
\[m\angle 1 = 99 - 20 = 79^\circ\]

Calculate the measure of angle 2

We substitute \(x = 11\) back into the expression for \(m\angle 2\):
\[m\angle 2 = x = 11^\circ\]
</reasoning>

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

\(m\angle 1 =\) <blank>\(79\)</blank>\(^\circ\) (Simplify your answer.)
\(m\angle 2 =\) <blank>\(11\)</blank>\(^\circ\) (Simplify your answer.)
</answer>

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Answer:

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<reasoning>

Set up the angle relationship

Using the Complementary Angles knowledge point, we know that two angles are complementary if the sum of their measures is exactly \(90^\circ\). From the given diagram, the measures of the two adjacent angles are:
\[m\angle 1 = 9x - 20\]
\[m\angle 2 = x\]
Since they are complementary, we write the equation:
\[(9x - 20) + x = 90\]

Solve for x

We combine the like terms and solve the linear equation:
\[10x - 20 = 90\]
\[10x = 110\]
\[x = 11\]

Calculate the measure of angle 1

We substitute \(x = 11\) back into the expression for \(m\angle 1\):
\[m\angle 1 = 9(11) - 20\]
\[m\angle 1 = 99 - 20 = 79^\circ\]

Calculate the measure of angle 2

We substitute \(x = 11\) back into the expression for \(m\angle 2\):
\[m\angle 2 = x = 11^\circ\]
</reasoning>

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

\(m\angle 1 =\) <blank>\(79\)</blank>\(^\circ\) (Simplify your answer.)
\(m\angle 2 =\) <blank>\(11\)</blank>\(^\circ\) (Simplify your answer.)
</answer>

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