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

To determine the type of triangle \( \triangle XYZ \), we first need to analyze the angles given. Since \( m \angle X = 56^{\circ} \) and \( m \angle Y = 68^{\circ} \), we can find \( m \angle Z \) by using the fact that the sum of the angles in a triangle is \( 180^{\circ} \). This gives us: \[ m \angle Z = 180^{\circ} - (56^{\circ} + 68^{\circ}) = 56^{\circ} \text{ (after calculation)} \] With all three angles being different (\( 56^{\circ}, 68^{\circ}, \text{ and } 56^{\circ} \)), the triangle is classified as isosceles because it has two equal angles. This will lead to two sides being of equal length. Additionally, since all the angles are less than \( 90^{\circ} \), \( \triangle XYZ \) is an acute triangle, as an acute triangle is defined as one that has all angles less than \( 90^{\circ} \). So, in summary, \( \triangle XYZ \) is an isosceles acute triangle!