Triangles ABC, EDC, and EFG are similar triangles. The measures of the three interior angles of triangle EFG are °, °, and °.

Because of the vertical angles theorem, BAC becomes 50°. And angle B is 180-(50+30)=100.

If all 3 triangles are similar, the angles of triangle EFG are 30°, 50°, 100°

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jajumonac jajumonac · Answer 2 · 2020-04-24T02:13:31+02:00

Answer:

The interior angles of triangle EFG are 30°, 50° and 100°.

Step-by-step explanation:

We know by given that [tex]\triangle ABC \sim \triangle EDC \sim \triangle EFG[/tex].

Similarities refers to proportional sides and congruent angles, so

[tex]\angle BAC \cong \angle DEC \cong \angle FEG[/tex], by corresponding elements.

Therefore, [tex]\angle BAC = 30\° =\angle DEC = \angle FEG[/tex]

By the same reason, [tex]\angle ECD = \angle ACB = \angle EGF = 50 \°[/tex]

Then,

[tex]\angle FEG + \angle EGF + \angle EFG = 180\°[/tex], by internal angles theorem.

Replacing values, we have

[tex]30\° + 50\° + \angle EFG = 180\°\\\angle EFG = 180\° -80\°\\\angle EFG = 100\°[/tex]

Therefore, the interior angles of triangle EFG are 30°, 50° and 100°.