Question

directions: order the angles from least to greatest for 13 - 14, then greatest to least for 15 - 16.
13.
14.

Explanation:

Step1: Recall the triangle angle - side relationship

In a triangle, the larger the side length, the larger the angle opposite it.

Step2: For triangle \(NRQ\)

The side lengths are \(17m\), \(21m\), \(24m\).
The angle opposite the side of length \(17m\) is \(\angle N\), the angle opposite the side of length \(21m\) is \(\angle R\), and the angle opposite the side of length \(24m\) is \(\angle Q\).
Since \(17<21<24\), then \(\angle N<\angle R<\angle Q\).

Step3: For triangle \(GJH\)

The side lengths are \(5in\), \(6in\), \(11in\).
The angle opposite the side of length \(5in\) is \(\angle G\), the angle opposite the side of length \(6in\) is \(\angle H\), and the angle opposite the side of length \(11in\) is \(\angle J\).
Since \(5 < 6<11\), then \(\angle G<\angle H<\angle J\).

Answer:

1. \(\angle N<\angle R<\angle Q\)
2. \(\angle G<\angle H<\angle J\)