list the angle measures of $ \triangle qrs $ in order from smallest to largest. assume that $ p $ is a positive number.

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Accepted Answer

# Explanation:
## Step1: Recall the triangle side - angle relationship
In a triangle, the larger the side length, the larger the angle opposite it.
## Step2: Compare the side lengths
We have side lengths $23p$, $56p$. Let's assume the third side (by triangle angle - side relationship). The side lengths (ignoring the non - variable part for comparison since $p>0$): $23p<56p$.
The angle opposite $23p$ is $\angle S$, the angle opposite $56p$ is $\angle Q$, and we know $\angle R = 92^{\circ}$.
Since $23p<56p$, then $m\angle S<m\angle Q$. And $m\angle S+m\angle Q=180^{\circ}-92^{\circ} = 88^{\circ}$ (sum of angles in a triangle is $180^{\circ}$).

# Answer:
$m\angle S<m\angle Q<m\angle R$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the triangle side - angle relationship

Step2: Compare the side lengths

Answer: