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

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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?)

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    2021-11-15T15:23:09+00:00

    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!

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