Question

in each case, use the new theorems to arrange the lettered measures from greatest to least. answer: angles from greatest to least are clear all

Explanation:

Step1: Recall angle - side relationship

In a triangle, the largest angle is opposite the longest side and the smallest angle is opposite the shortest side.

Step2: Identify side - angle pairs

The side lengths are 5 cm, 9 cm, and 12 cm. Angle $\alpha$ is opposite the 9 - cm side, angle $\beta$ is opposite the 12 - cm side, and angle $\gamma$ is opposite the 5 - cm side.

Step3: Arrange angles

Since 12>9>5, the angles from greatest to least are $\beta$, $\alpha$, $\gamma$.

Answer:

$\beta$, $\alpha$, $\gamma$