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belka [17]
3 years ago
15

I NEED ASAP: What is the value of x?

Mathematics
1 answer:
Vitek1552 [10]3 years ago
6 0

Answer:

x=48

Step-by-step explanation:

10x-20+6x+8=180 set the equations together and to equal 180 since a line is 180 degrees

Get the variables together

10x-20+6x+8=180

-6x       -6x

4x-20+8=180

add together -20 and 8

4x-12=180

add -12 on each side

4x-12=180

   +12  +12

4x=192

divide all by 4

x=48

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7 0
3 years ago
In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.
krek1111 [17]

Answer:

AC = 14 sqrt(2) = 19.80    

Step-by-step explanation:

Below is the diagram showing you how this has been set up. The figure is a trapezoid which means BC and AD are parallel. AC is a transversal of the parallel lines.

Givens

  • <ABC = <ACD                          
  • ABCD  is a trapezoid
  • BC = 14
  • AD = 28
  • AC is a transversal of BC and AD

Solution

  • <ABC = <ACD                Given
  • <DAC = <ACB                Alternate interior angles.
  • ΔACB ≅ΔDAC               AA
  • <BAC = <ADC                Angles of similar triangles are equal
  • AC /28 = 14/AC              Form a proportion from corresponding sides
  • AC*AC = 14 * 28             Cross multiply the proportion. Combine
  • AC^2 = 392                    Express as prime factors.
  • AC^2 = 7*7*2*2*2           Take the square root of both sides
  • sqrt(AC)^2 = sqrt(7*7*2*2*2)
  • AC = 7*2 * sqrt(2)
  • AC = 14 sqrt(2) = 19.80    

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Step-by-step explanation:

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Step-by-step explanation:

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