Question

do = 7 cm, og = 5 cm, dg = 6 cm
arrange the angles from smallest to largest based on their measures.
∠o, ∠d, ∠g
∠d, ∠g, ∠o
∠o, ∠g, ∠d
∠d, ∠o, ∠g

Explanation:

Step1: Recall the triangle side - angle relationship

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

Step2: Identify the side lengths and their opposite angles

In \(\triangle DOG\), \(OG = 5\mathrm{cm}\), \(DG=6\mathrm{cm}\), \(DO = 7\mathrm{cm}\). The angle opposite \(OG\) is \(\angle D\), the angle opposite \(DG\) is \(\angle O\), and the angle opposite \(DO\) is \(\angle G\).

Step3: Compare the side lengths

Since \(OG\lt DG\lt DO\) (i.e., \(5\lt6\lt7\)).

Step4: Determine the angle order

By the side - angle relationship, the angles opposite these sides follow the order \(\angle D\lt\angle O\lt\angle G\)

Answer:

\(\angle D,\angle O,\angle G\)