Question

determine an expression for \\(x\\) based on the following diagram:

diagram showing a triangle with an exterior angle. the interior angles are labeled as \\(x^\circ\\) at the top and \\(7^\circ\\) at the bottom-left. the exterior angle at the bottom-right is labeled as \\(4a - 1\\).

\\(x = -2a + 8\\)
\\(x = 6a - 6\\)
\\(x = 2a - 8\\)
\\(x = 6a + 6\\)

Explanation:

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<reasoning>

Identify the given angles in the diagram

Using the Exterior Angle Theorem knowledge point
\[

$$\begin{aligned} &\text{Interior Angle 1: } 7\\ &\text{Interior Angle 2: } x\\ &\text{Exterior Angle: } 6a - 1 \end{aligned}$$

\]

Set up the exterior angle equation

Using the Exterior Angle Theorem knowledge point
\[

$$\begin{aligned} &7 + x = 6a - 1 \end{aligned}$$

\]

Solve for x

Using the Exterior Angle Theorem knowledge point
\[

$$\begin{aligned} &x = 6a - 1 - 7\\ &x = 6a - 8 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(x = -2a + 8\)</mcq-option>
<mcq-option>(B) \(x = 6a - 6\)</mcq-correct>
<mcq-correct>(C) \(x = 2a - 8\)</mcq-correct>
<mcq-option>(D) \(x = 6a + 6\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given angles in the diagram

Using the Exterior Angle Theorem knowledge point
\[

$$\begin{aligned} &\text{Interior Angle 1: } 7\\ &\text{Interior Angle 2: } x\\ &\text{Exterior Angle: } 6a - 1 \end{aligned}$$

\]

Set up the exterior angle equation

Using the Exterior Angle Theorem knowledge point
\[

$$\begin{aligned} &7 + x = 6a - 1 \end{aligned}$$

\]

Solve for x

Using the Exterior Angle Theorem knowledge point
\[

$$\begin{aligned} &x = 6a - 1 - 7\\ &x = 6a - 8 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(x = -2a + 8\)</mcq-option>
<mcq-option>(B) \(x = 6a - 6\)</mcq-correct>
<mcq-correct>(C) \(x = 2a - 8\)</mcq-correct>
<mcq-option>(D) \(x = 6a + 6\)</mcq-option>
</answer>

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