Question

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

Answer 1

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°

Answer 2

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

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°.