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2 years ago

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

Mathematics

2 answers:

iren [92.7K]2 years ago

7 0

Answer:

<h2>The interior angles of triangle EFG are 30°, 50° and 100°.</h2>

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°.

Misha Larkins [42]2 years ago

4 0

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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2 years ago

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Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

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Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula $f(n+1)=f(n)+2.5$

Explanation:

The given recursive formula is $f(n+1)=f(n)+2.5$ for $n\geq 1$ and $f(1)=-10$

We need to determine the sequence.

The sequence can be determined by substituting n = 1, 2, 3, 4,....

2nd term of the sequence:

Substituting n = 1 in the formula $f(n+1)=f(n)+2.5$ , we get,

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Simplifying, we have,

$f(2)=-10+2.5=-7.5$

Thus, the 2nd term of the sequence is -7.5

3rd term of the sequence:

Substituting n = 2 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(2+1)=f(2)+2.5$

Simplifying, we have,

$f(3)=-7.5+2.5=-5$

Thus, the 3rd term of the sequence is -5

4th term of the sequence:

Substituting n = 3 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(3+1)=f(3)+2.5$

Simplifying, we have,

$f(4)=-5+2.5=-2.5$

Thus, the 4th term of the sequence is -2.5

Therefore, the sequence is –10, –7.5, –5, –2.5, …

Hence, Option C is the correct answer.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

We know that:

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