list the angle measures of $\triangle ijk$ in order from smallest to largest. assume that $v$ is a positive number.
$m\angle\square

Question

list the angle measures of $\triangle ijk$ in order from smallest to largest. assume that $v$ is a positive number.
$m\angle\square < m\angle\ < m\angle$

Accepted Answer

# Explanation:
## Step1: Recall the triangle side - angle relationship
In a triangle, the larger the length of a side, the larger the measure of the opposite angle. So we first need to determine the lengths of the sides (in terms of $v$) and then find the opposite angles.

The sides of $\triangle IJK$ are: $IJ = 15v$, $JK=19v$, and $IK = 20v$. Since $v>0$, we can compare the lengths of the sides by comparing the coefficients of $v$.

We have $15v<19v<20v$, so $IJ < JK<IK$.

## Step2: Find the opposite angles
- The angle opposite to side $IJ$ is $\angle K$ (because side $IJ$ is between $I$ and $J$, so the opposite angle is $\angle K$).
- The angle opposite to side $JK$ is $\angle I$ (because side $JK$ is between $J$ and $K$, so the opposite angle is $\angle I$).
- The angle opposite to side $IK$ is $\angle J$ (because side $IK$ is between $I$ and $K$, so the opposite angle is $\angle J$).

Since $IJ < JK<IK$, by the side - angle relationship in a triangle (larger side opposite larger angle), we have $m\angle K<m\angle I < m\angle J$.

# Answer:
$m\angle K<m\angle I < m\angle J$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the triangle side - angle relationship

Step2: Find the opposite angles

Answer: