Question

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

Answer 1

Answer:

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

Step-by-step explanation:

We know by given that $\triangle ABC \sim \triangle EDC \sim \triangle EFG$.

Similarities refers to proportional sides and congruent angles, so

$\angle BAC \cong \angle DEC \cong \angle FEG$, by corresponding elements.

Therefore, $\angle BAC = 30\° =\angle DEC = \angle FEG$

By the same reason, $\angle ECD = \angle ACB = \angle EGF = 50 \°$

Then,

$\angle FEG + \angle EGF + \angle EFG = 180\°$, by internal angles theorem.

Replacing values, we have

$30\° + 50\° + \angle EFG = 180\°\\\angle EFG = 180\° -80\°\\\angle EFG = 100\°$

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

Answer 2

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°