Question

identify the sides of △nop. see examples 3 and 4.

1. which side is the longest?
2. which side is the shortest?

Explanation:

Step1: Find the measure of angle \(O\)

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle N = 66^{\circ}\), \(\angle P=60^{\circ}\). Then \(\angle O=180^{\circ}-\angle N - \angle P\).

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Step2: Relate angles and sides

In a triangle, the larger the angle, the longer the side opposite it. We have \(\angle N = 66^{\circ}\), \(\angle P = 60^{\circ}\), \(\angle O=54^{\circ}\).
The side opposite \(\angle N\) is \(OP\), the side opposite \(\angle P\) is \(ON\), and the side opposite \(\angle O\) is \(NP\).

Answer:

1. The longest side is \(OP\) (opposite the largest angle \(\angle N = 66^{\circ}\)).
2. The shortest side is \(NP\) (opposite the smallest angle \(\angle O = 54^{\circ}\)).