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topjm [15]
3 years ago
8

USLUIT il Find x. 45° 30°

Mathematics
1 answer:
IceJOKER [234]3 years ago
7 0

Answer:

111°

Step-by-step explanation:

  • All these are parallel lines, so the 36° angle is equal to the 36° angle inside the big triangle because they are vertically opposite.

  • Ignore the line cutting between 45° and the 30° and consider it as one triangle
  • Add them to get 75°
  • Now you have two known angles 75° and 36°
  • To get angle <em>x</em><em> </em>add 75° and 36° to get 111°
  • Because x° is an exterior angle and exterior angles equal to the sum of interior angles opposite it inside the triangle.
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Answer:

The sum of the internal ángles = 360°

(3y+40)°  and  (3x-70°) are suplementary angles = 180°

then:

(3x-70) + (3y+40) + 120 + x = 360     ⇒ first eq.

(3y+40) + (3x-70) = 180      ⇒  second eq

development:

from the first eq.

3x + x + 3y  =  360  + 70 - 40 - 120

4x + 3y = 430 - 160

4x + 3y = 270       ⇒  third eq.

3y = 270 - 4x

y = (270 - 4x) / 3    ⇒  fourth eq.

from the secon eq.:

3y + 3x = 180 + 70 - 40

3y + 3x = 250 - 40

3y + 3x = 210    ⇒  fifth eq.

multiply by -1  the fifth eq and sum with the third eq.

  -3y  - 3x = -210    ⇒   (fifth eq. *-1)

   3y  + 4x = 270

⇒  0   +  x  = 60

x = 60°

from the fourth eq.

y = (270-4x)/3

y = (270-(4*60)) / 3

y = (270 - 240) / 3

y = 30/3

y = 10°

Probe:

from the first eq.

(3x-70) + (3y+40) + 120 + x = 360

3*60 - 70 + 3*10 + 40 + 120 + 60 = 360

180 - 70 + 30 + 40 + 120 + 60 = 360

180 + 30 + 40 + 120 + 60 - 70 = 360

430 - 70 = 360

Answer:

y = 10

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3 years ago
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Formula is same as before

y-1=3x-6

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