Question

In ΔLMN, MN = 8, NL = 13, and LM = 9. Which statement about the angles of ΔLMN must be true?

Answer 1

In ΔLMN, the largest angle is opposite the longest side NL, making angle M the largest, while the smallest angle is opposite the shortest side LM, which is angle N.

Step-by-step explanation:

In ΔLMN, with sides MN = 8, NL = 13, and LM = 9, we can determine which statements about the angles must be true using the knowledge that the largest side of a triangle is opposite the largest angle. Here, side NL is the longest, which means that angle M, the angle opposite NL, must be the largest angle in the triangle.

By the same token, since LM is the shortest side, angle N opposite side LM must be the smallest angle in the triangle. Therefore, the relationship between the sides and angles in ΔLMN will be such that:

• Angle M > Angle L > Angle N
• Angle N is the smallest angle.
• Angle M is the largest angle.