Question

given that the following triangles are congruent, determine the value of \\(x\\):

\\(x = 1\\)
\\(x = 396\\)
\\(x = 11\\)
\\(x = \frac{28}{3}\\)

Explanation:

Identify corresponding parts of the congruent triangles

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Calculate the corresponding angle in the right triangle

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Solve for x

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(Self-correction: Let's re-verify the corresponding angles based on side lengths)

• Left triangle sides: triple tick (left), double tick (top-right), single tick (bottom-right, labeled \(6x-6\)).
• Right triangle sides: triple tick (right), double tick (bottom-left), single tick (top-left).
• In the left triangle, the angle \(6x-6\) is between the triple-tick side and the single-tick side.
• In the right triangle, the angle between the triple-tick side and the single-tick side is \(60^\circ\).
• Therefore, the corresponding angle to \(6x-6\) is \(60^\circ\).

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Answer:

• (A) \(x = 1\)
• (B) \(x = 396\)
• (C) \(x = 11\) (Correct answer)
• (D) \(x = \frac{28}{3}\)