Question

question
in △efg, m∠e = 107° and m∠f = 51°. which list has the sides of △efg in order from shortest to longest?
answer
○ ge, ef, fg
○ fg, ge, ef
○ fg, ef, ge
○ ef, ge, fg
○ ge, fg, ef
○ ef, fg, ge
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Explanation:

Step1: Find the measure of the third angle

In a triangle, the sum of angles is \(180^{\circ}\). Let \(\angle G=x\). Then \(x + 107^{\circ}+51^{\circ}=180^{\circ}\). So \(x=180^{\circ}-(107^{\circ}+51^{\circ}) = 22^{\circ}\).

Step2: Apply the side - angle relationship

In a triangle, the larger the angle, the longer the side opposite it. Since \(\angle G = 22^{\circ}\), \(\angle F=51^{\circ}\), \(\angle E = 107^{\circ}\), and the side opposite \(\angle G\) is \(EF\), the side opposite \(\angle F\) is \(GE\), the side opposite \(\angle E\) is \(FG\). So \(EF\lt GE\lt FG\).

Answer:

EF, GE, FG