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 angle l angle m angle n

Explanation:

Step1: Recall the triangle angle - side relationship

In a triangle, the larger the length of a side, the larger the angle opposite that side, and the smaller the length of a side, the smaller the angle opposite that side. That is, if in $\triangle ABC$, $a,b,c$ are the lengths of the sides opposite to $\angle A,\angle B,\angle C$ respectively, then if $a > b>c$, $\angle A>\angle B >\angle C$.

Step2: Identify the sides and their opposite angles

• Side $LN = 24$ in, opposite angle $M$.
• Side $MN=25$ in, opposite angle $L$.
• Side $LM = 27$ in, opposite angle $N$.

Step3: Order the sides by length

We have $24<25 < 27$, so $LN

Step4: Order the angles by size

Since the side opposite angle $M$ is the shortest ($LN = 24$), angle $M$ is the smallest. Since the side opposite angle $N$ is the longest ($LM=27$), angle $N$ is the largest.

Answer:

The smallest angle of the triangle is angle M.
The largest angle of the triangle is angle N.