Question

1. list the angles in the triangle from largest to smallest.

Explanation:

Step1: Recall the triangle angle - side relationship

In a triangle, the larger the side length, the larger the angle opposite to it. The side lengths of the triangle are: \(NP = 18\), \(PQ=12\), and \(NQ = 24\).

Step2: Identify the angles opposite each side

• The angle opposite to \(PQ = 12\) is \(\angle N\).
• The angle opposite to \(NP=18\) is \(\angle Q\).
• The angle opposite to \(NQ = 24\) is \(\angle P\).

Since \(24>18 > 12\), the angles opposite to these sides will follow the same order. So \(\angle P>\angle Q>\angle N\) (because \(\angle P\) is opposite \(NQ = 24\), \(\angle Q\) is opposite \(NP = 18\), and \(\angle N\) is opposite \(PQ=12\)). Wait, looking at the options, the vertices are \(P\), \(Q\), \(N\). Let's re - check the side - angle correspondence:

• Side \(PQ = 12\), opposite angle \(\angle N\)
• Side \(NP=18\), opposite angle \(\angle Q\)
• Side \(NQ = 24\), opposite angle \(\angle P\)

So the order of angles from largest to smallest: \(\angle P\), \(\angle Q\), \(\angle N\) (since \(NQ>NP>PQ\), so \(\angle P>\angle Q>\angle N\)). Looking at the options, the first option is \(P,Q,N\).

Answer:

A. \(P,Q,N\) (assuming the first option is labeled as A, since the options are \(P,Q,N\); \(N,P,Q\); \(Q,N,P\); \(P,N,Q\) and we derived the order \(P > Q> N\))