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To solve for \( x \) in these geometric problems, you'll generally need to apply the rules of geometry, such as the properties of triangles (e.g., angle sum property, isosceles triangle properties), the Pythagorean theorem, and similar triangles. Here’s a general approach for each type of problem you might see: 1. **Angle Problems**: Use the fact that the sum of angles in a triangle is \(180^\circ\). 2. **Pythagorean Theorem**: For right triangles, use \(a^2 + b^2 = c^2\). 3. **Isosceles Triangles**: The angles opposite the equal sides are equal. 4. **Equilateral Triangles**: All sides and angles are equal. Each angle is \(60^\circ\). 5. **Finding Missing Lengths**: Use similar triangles or properties of special right triangles, like \(30^\circ{-}60^\circ{-}90^\circ\) and \(45^\circ{-}45^\circ{-}90^\circ\) triangles. Since I can't process images to identify each problem step-by-step, please provide a specific problem or more details, and I can assist you further!