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 x, z, y.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Given two angles 42° and 84°. Let the unknown angle be $\theta$. Then $\theta=180-(42 + 84)$.

Step2: Calculate the unknown angle

$\theta=180 - 126=54^{\circ}$.

Step3: Recall the angle - side relationship in a triangle

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°, 54°, 84°. The sides opposite these angles are $x$, $z$, $y$ respectively. 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.