Describe the triangle $$ (\triangle X Y Z $$, not shown) as scalene, isosceles, or equil.............................................................. $$ m \angle X=56^{\circ} \text { and } m \angle Y=68^{\circ} $$ scalene triangle isosceles triangle equilateral triangle Is the triangle acute, right, or obtuse? acute triangle right triangle obtuse triangle

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To classify triangle $$ \triangle XYZ $$ based on the given information:

1. **Given Angles:**
   - $$ m \angle X = 56^{\circ} $$
   - $$ m \angle Y = 68^{\circ} $$

2. **Determine the Third Angle:**
   - The sum of angles in any triangle is $$ 180^{\circ} $$.
   $$
   m \angle Z = 180^{\circ} - (56^{\circ} + 68^{\circ}) = 56^{\circ}
   $$

3. **Classification by Sides:**
   - **Isosceles Triangle:** A triangle with at least two equal sides (and consequently, at least two equal angles).
   - **Equilateral Triangle:** A triangle with all three sides (and angles) equal.
   - **Scalene Triangle:** A triangle with all sides (and angles) of different lengths.

Since $$ m \angle X = m \angle Z = 56^{\circ} $$, sides $$ XY $$ and $$ YZ $$ are equal.

**Conclusion:** $$ \triangle XYZ $$ is an **isosceles triangle**.

4. **Classification by Angles:**
   - **Acute Triangle:** All angles are less than $$ 90^{\circ} $$.
   - **Right Triangle:** One angle is exactly $$ 90^{\circ} $$.
   - **Obtuse Triangle:** One angle is greater than $$ 90^{\circ} $$.

The angles of $$ \triangle XYZ $$ are $$ 56^{\circ} $$, $$ 68^{\circ} $$, and $$ 56^{\circ} $$, all of which are less than $$ 90^{\circ} $$.

**Conclusion:** $$ \triangle XYZ $$ is an **acute triangle**.

---

**Final Classification:**
- **Type by Sides:** Isosceles Triangle
- **Type by Angles:** Acute Triangle
The triangle is an isosceles triangle and an acute triangle.

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