In any triangle, the angles opposite the longer sides are larger, while the angles opposite shorter sides are smaller. Therefore, to determine the order of the angles based on the triangle's side lengths, we would first need information about the specific side lengths of triangle \( \triangle ABC \).
However, since the only provided information is that the perimeter is 60 units, we can only make general conclusions about the measures of angles based on hypothetical lengths of the sides.
For the ordering of the angles in terms of their measures based on the sides:
- If side \( a \) is opposite angle \( A \),
- side \( b \) is opposite angle \( B \),
- and side \( c \) is opposite angle \( C \),
the relationships would be:
- If \( a < b < c \), then \( m\angle A < m\angle B < m\angle C \).
- If \( c < b < a \), then \( m\angle C < m\angle B < m\angle A \), and so forth.
Without the specific side lengths, we can't determine the specific order of the angles. However, we could tell you the relationship based on the triangle inequality that ensures that the angles should add up to 180°, and correspondingly, the longest side should be opposite the largest angle.
If you assume the sides were given to you as \( a = 15, b = 20, c = 25 \) (adding up to 60), you would find that:
- \( m\angle A < m\angle B < m\angle C \) since side \( a \) is the shortest and side \( c \) is the longest.
Hence, the choice for the ordered angles based on side lengths and corresponding angles would be:
- \( m\angle A < m\angle B < m\angle C \).
You would select the corresponding option for your question accordingly.
For just reflection on standard responses: if there were no contradiction in assigning values to sides, you may choose an option based on your triangle's side lengths if provided.
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