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The second angle of a triangle is 20 degrees greater than the first angle. The third angle is twice the second. Find the three angles. (Note: in any triangles, angle measures add up to … how many degrees?)

Respuesta :

A triangles angles add up to 180 degrees. Using this knowledge, we can write an equation evaluating the first angle as x.
x + x + 20 + 2(x + 20) = 180
distribute the 2
x + x + 20 + 2x + 40 = 180
combine like terms
4x + 60 = 180
isolate the variable: subtract 26 from both sides
4x = 120
isolate the variable: divide each side by 4
x = 30
We can now determine the other sides using this information:
Side 1: 30 degrees
to get side 2 we need to add 20 to side 1 getting:
Side 2: 50
For the last one, we must multiply side 2 by 2 getting:
Side 3: 100

condensed:
side 1: 30
side 2: 50
side 3: 100

We can check this by adding all of our answers and seeing if they equal 180:
30 + 50 + 100 =180

Hope this helps!
fichoh

Using the triangle theorem, the three angles in the triangle are 30°, 50°, 100°

Let the angles in the triangle be represented thus :

  • First angle = x
  • Second angle = x + 20
  • Third angle = 2(x + 20)

Using the variables to createvthe triangle theorem :

x + x + 20 + 2(x + 20) = 180

2x + 20 + 2x + 40 = 180

4x + 60 = 180

4x = 180 - 60

4x = 120

x = 120 / 40

x = 30°

Second angle = (x + 20) = 30 + 20 = 50°

Third angle = 2(x + 20) = 2(50) = 100°

Therefore, the three angles are 30, 50, 100

Learn more : https://brainly.com/question/19060921

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