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shusha [124]
2 years ago
5

4

Mathematics
1 answer:
Natali [406]2 years ago
8 0

The ratio of the area of ∆ABC to the area of ∆DEF is; 1:100.

<h3>What is the ratio of the area of ∆ABC to the area of ∆DEF?</h3>

Since, a major criterion for similarity and congruence of triangles is that the ratio of corresponding sides are equal.

On this note, since the task content suggest that the ratio of the perimeters is; 1:10, it follows from conventional mathematics that the ratio of their areas is given as; 1²:10²; 1:100.

Read more on congruent triangles;

brainly.com/question/9217675

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Use the diagram below to solve. The m∠ 1 = 29x + 12 and the m∠ 5 = 15x - 8. All lines that appear parallel are parallel.
Kamila [148]

Answer:

Equation: (29x + 12)° + (15x - 8)° = 180°

x = 4

m∠ 5 = 52°

Step-by-step explanation:

Given:

m∠ 1 = 29x + 12,

m∠ 5 = 15x - 8

Since all lines that appear are parallel, therefore, opposite angles of the quadrilateral are congruent.

Therefore, m<1 = m<4 = 29x + 12

m<4 + m<5 = 180° (linear pair)

(29x + 12) + (15x - 8) = 180° (substitution)

The equation above is what we would use in solving for x. Let's solve for x:

29x + 12 + 15x - 8 = 180

Collect like terms

44x + 4 = 180

Subtract 4 from both sides

44x = 180 - 4

44x = 176

Divide both sides by 44

x = 176/44

x = 4

m∠ 5 = 15x - 8

Plug in the value of x

m∠ 5 = 15(4) - 8 = 60 - 8

m∠ 5 = 52°

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