1. The problem asks to classify triangles by their sides and angles, and to find angle measures and classify triangles by angles. 2. For the right triangle XYZ with right angle at Y and equal sides XY and YZ, since two sides are equal, it is an isosceles right triangle. 3. For triangle LMN with sides LM = LN (one hash mark each) and MN different (two hash marks), it is isosceles by sides. 4. To find angle measures given 20°, 125°, and 35°, note that these angles sum to 180°: $$20 + 125 + 35 = 180$$, so they form a triangle. 5. Classify the triangle by angles: since one angle is 125° > 90°, it is an obtuse triangle. 6. For the figure with angle 64° and unknown angle x, if it is a triangle, use the triangle sum rule: $$x + 64 + y = 180$$. Without y, cannot solve further. 7. Summary: - Triangle XYZ: isosceles right triangle (two equal sides, one right angle). - Triangle LMN: isosceles triangle (two equal sides). - Triangle with angles 20°, 125°, 35°: obtuse triangle.