Question

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

Explanation:

Identify corresponding angles and sides

Using the Similar Triangles knowledge point

• The first triangle has angles \(41^\circ\) and \(83^\circ\).
• The second triangle has angles \(41^\circ\) and \(83^\circ\).
• In the first triangle, the side of length \(15\) is between the \(41^\circ\) and \(83^\circ\) angles.
• In the second triangle, the side of length \(10\) is between the \(41^\circ\) and \(83^\circ\) angles.
• Therefore, the side of length \(15\) corresponds to the side of length \(10\).
• In the first triangle, the side of length \(18\) is opposite the \(83^\circ\) angle.
• In the second triangle, the side of length \(x\) is opposite the \(83^\circ\) angle.
• Therefore, the side of length \(18\) corresponds to the side of length \(x\).

Set up the similarity ratio

Using the Corresponding Sides Ratio knowledge point

$$ \frac{15}{10} = \frac{18}{x} $$

Solve for x

Using the Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Answer:

These triangles are similar. Solve for x.

\(x =\) <blank>12</blank>