Question

find the values of \\(x\\) and \\(y\\) in the following diagram:

Explanation:

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<reasoning>

Find the value of y

Using the Triangle Angle Sum Theorem knowledge point
\[

$$\begin{aligned} 90^\circ + 50^\circ + (8y)^\circ &= 180^\circ \\ 140 + 8y &= 180 \\ 8y &= 40 \\ y &= 5 \end{aligned}$$

\]

Find the value of x

Using the Supplementary Angles knowledge point
\[

$$\begin{aligned} (8y)^\circ + (5x + 55)^\circ &= 180^\circ \\ 8(5) + 5x + 55 &= 180 \\ 40 + 5x + 55 &= 180 \\ 5x + 95 &= 180 \\ 5x &= 85 \\ x &= 17 \end{aligned}$$

\]
</reasoning>

<answer>
\(x = 17\), \(y = 5\)
</answer>

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Answer:

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<reasoning>

Find the value of y

Using the Triangle Angle Sum Theorem knowledge point
\[

$$\begin{aligned} 90^\circ + 50^\circ + (8y)^\circ &= 180^\circ \\ 140 + 8y &= 180 \\ 8y &= 40 \\ y &= 5 \end{aligned}$$

\]

Find the value of x

Using the Supplementary Angles knowledge point
\[

$$\begin{aligned} (8y)^\circ + (5x + 55)^\circ &= 180^\circ \\ 8(5) + 5x + 55 &= 180 \\ 40 + 5x + 55 &= 180 \\ 5x + 95 &= 180 \\ 5x &= 85 \\ x &= 17 \end{aligned}$$

\]
</reasoning>

<answer>
\(x = 17\), \(y = 5\)
</answer>

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