Question

Use the relationship between the side lengths and the angles opposite those sides. What are the smallest and largest angles of △LMN? The smallest angle of the triangle is . The largest angle of the triangle is

Answer 1

Answer:

Angle M is the smallest Angle/ Angle N is the longest Angle

Step-by-step explanation:

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Answer 2

Let us take a random triangle we call $\Delta LMN$ for a better understanding of the solution provided here.

A diagram of the $\Delta LMN$ is attached here.

The rule to be applied here is the relationship between the side lengths of a triangle and the angles opposite those sides. This relationship states that:

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

Let us verify this using the diagram attached.

As per the diagram, the smallest interior angle is $\angle L$ and the side opposite to it, $MN=24$ has the smallest side just as the relationship had suggested.

Likewise, the largest interior angle is $\angle N=108^0$ and the side opposite to it, LM=45.7 is the longest side just as the relationship had suggested.

This rule/relationship can be applied to any triangle in question.