Question

these triangles are similar.
solve for x.
\\(x = \\)

Explanation:

Identify corresponding sides using angle markers

Using the Similar Triangles knowledge point

• In the larger triangle, the side of length \(30\) is adjacent to the angles \(41^\circ\) and \(56^\circ\).
• In the smaller triangle, the side of length \(12\) is adjacent to the angles \(41^\circ\) and \(56^\circ\).
• Therefore, the side of length \(30\) corresponds to the side of length \(12\).

Match the remaining corresponding sides

Using the Similar Triangles knowledge point

• In the larger triangle, the side of length \(20\) is adjacent to the angle \(56^\circ\) and the unmarked angle.
• In the smaller triangle, the side of length \(x\) is adjacent to the angle \(56^\circ\) and the unmarked angle.
• Therefore, the side of length \(20\) corresponds to the side of length \(x\).

Set up and solve the proportion

Using the Corresponding Sides Ratio knowledge point

$$ \frac{x}{20} = \frac{12}{30} $$

$$ x = 20 \cdot \frac{12}{30} = 20 \cdot \frac{2}{5} = 8 $$

Answer:

These triangles are similar. Solve for x.
\(x =\) <blank>8</blank>