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    Write an inequality in the variable x for the degree measure of the smallest angle of a triangle given that the degree measure of the smallest angle is at most 30 degrees

    diagram
    top angle x+8
    bottom left x
    right angle has ?

    © BrainMass Inc. brainmass.com December 24, 2021, 9:23 pm ad1c9bdddf
    https://brainmass.com/math/triangles/building-a-ski-ramp-373419

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    The third angle in the given triangle = 180° - (x + x + 8) = 180° - 2x - 8° = 172° - 2x
    We know that for any positive value of x, x < x + 8
    Now consider x and 172 - 2x
    Depending upon the value of x, either x becomes the smallest angle or 172 - 2x becomes the smallest angle
    (a) Assuming x to be the smallest angle, the inequality is obviously 0 < x ≤ 30
    (b) Assuming 172 - 2x to be the smallest angle, the inequality is 0 < 172 - 2x ≤ 30
    172 - 2x > 0
    172 > 2x
    2x < 172
    x < 86
    Again, 142 ≤ 2x
    2x ≥ 142
    x ≥ 71
    So, assuming 172 - 2x to be the smallest angle, the inequality is 71 ≤ x < 86
    Answer: {x | 0 < x ≤ 30 or 71 ≤ x < 86}

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:23 pm ad1c9bdddf>
    https://brainmass.com/math/triangles/building-a-ski-ramp-373419

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