Question

determine the unknown angle measure for triangle xyz (with angles 42°, 84°) and then list the sides x, y, z in order from shortest to longest. the unknown angle is 54°, and the order is x, z, y. the unknown angle is 54°, and the order is x, y, z. the unknown angle is 54°, and the order is z, x, y. the unknown angle is 54°, and the order is y, x, z.

Explanation:

Step1: Find the unknown angle

The sum of angles in a triangle is 180°. Let the unknown angle be $\theta$. So, $\theta=180^{\circ}-42^{\circ}-84^{\circ}=54^{\circ}$.

Step2: Order the sides

In a triangle, the side opposite the smallest - angle is the shortest and the side opposite the largest - angle is the longest. The angles in ascending order are $42^{\circ},54^{\circ},84^{\circ}$. The side opposite the $42^{\circ}$ angle is $x$, the side opposite the $54^{\circ}$ angle is $z$, and the side opposite the $84^{\circ}$ angle is $y$. So the order of the sides from shortest to longest is $x,z,y$.

Answer:

The unknown angle is 54°, and the order is x, z, y.