Algebra

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The following problem must be solved 3 different ways in which X=smallest angle for problem 1. Problem 2 would be X=medium sized angle. Problem 3 would start with X=largest angle. I was able to figure out X=smallest angle, but I am stumped on the other 2 as to how to set it up.

In a triangle the measure of the medium-sized angle is 3 times the measure of the smallest angle and half the measure of the largest angle. What are the measures of the 3 angles?

  • Algebra -

    I will do the first, and start you off on the second

    method1:
    smallest angle -- x
    medium-sized angle -- 3x
    larges angle --- 6x

    x + 3x + 6x = 180
    10x = 180
    x = 18
    3x = 54
    6x = 108 , not 108+54+18 = 180

    method 2:
    medium sized angle = x
    small angle = (1/3)x
    large angle = 2x

    x + (1/3)x + 2x = 180
    multiply by 3
    3x + x + 6x = 540
    10x = 540
    x = 54
    (1/3)x = 18
    2x = 108 , notice we got the same answers

    you do the 3rd way.

  • Algebra -

    Reiny...yes, thank you. I appreciate the help so much. I did have the some work-up for X=smallest angle. Thanks for starting me out for the next 2 angles.

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