Describe the triangle ( $$ \triangle X Y Z $$, not shown) as scalene, isosceles, or equilateral. $$ \mathrm{m} \angle X=\mathrm{m}_{\angle} Y=24^{\circ} $$ scalene triangle isosceles triangle equilateral triangle Is the triangle acute, right, or obtuse? acute triangle right triangle obtuse triangle

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Given triangle $$ \triangle XYZ $$ with the following angle measures:
$$
\mathrm{m} \angle X = \mathrm{m} \angle Y = 24^{\circ}
$$

### Classification by Sides:
- **Isosceles Triangle**: 
  - A triangle is **isosceles** if at least two sides (and consequently, at least two angles) are equal.
  - Since $$ \angle X = \angle Y $$, sides $$ XY $$ and $$ XZ $$ (opposite these angles) are equal.
  - **Conclusion**: $$ \triangle XYZ $$ is an **isosceles triangle**.

### Classification by Angles:
1. **Determine the Third Angle**:
   $$
   \mathrm{m} \angle Z = 180^{\circ} - (\mathrm{m} \angle X + \mathrm{m} \angle Y) = 180^{\circ} - (24^{\circ} + 24^{\circ}) = 132^{\circ}
   $$
   
2. **Determine the Type of Triangle**:
   - **Acute Triangle**: All angles are less than $$ 90^{\circ} $$.
   - **Right Triangle**: One angle is exactly $$ 90^{\circ} $$.
   - **Obtuse Triangle**: One angle is greater than $$ 90^{\circ} $$.

- Since $$ \angle Z = 132^{\circ} > 90^{\circ} $$, $$ \triangle XYZ $$ has an **obtuse angle**.
   
   - **Conclusion**: $$ \triangle XYZ $$ is an **obtuse triangle**.

### Summary:
- **Type by Sides**: Isosceles Triangle
- **Type by Angles**: Obtuse Triangle
The triangle is an isosceles triangle and an obtuse triangle.

Describe the triangle ( \( \triangle X Y Z \), not shown) as scalene, isosceles, or equilateral. \[ \mathrm{m} \angle X=\mathrm{m}_{\angle} Y=24^{\circ} \] scalene triangle isosceles triangle equilateral triangle Is the triangle acute, right, or obtuse? acute triangle right triangle obtuse triangle

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