Lines a and b are parallel and lines e and f are parallel.

Mathematics

2 answers:

salantis [7]3 years ago

7 0

Answer:

Step-by-step explanation:

Alternate exterior angles where the transversal "e" crosses parallel lines "a" and "b" are congruent. x° ≅ 82°

ICE Princess25 [194]3 years ago

5 0

Answer: second option.

Step-by-step explanation:

It is important to remember that Vertical angles are defined as two non-adjacent angles formed by intersecting lines. These angles share the same vertex and they are congruent.

Observe the figure attached. Since lines "a" and "b" are parallel, you can notice that the angle 82° angle x° are Vertical angles. Therefore, they are congruent.

Then, the value of "x" is:

$x=82\°$

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Flauer [41]

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a = 5 cm

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p = 11:2 = 5.5

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3. Find the area of the equilateral triangle whose each side is 8 cm.

a = b = c = 8 cm

p = (8•3):2 = 12 cm

$A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2$

4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

a = 2x

b = 3x

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p = 32:2 = 16 cm

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