Math I need help asap thanks.?

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The second angle of a triangle is 3 times as large as the first. The third angle is 75° more than the first. Find the measure of the smallest angle.

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  • 1 decade ago
    Favorite Answer

    s=3f

    t=75+f

    s+f+t=180

    3f+f+75+f=180

    5f=105

    f=21

  • 1 decade ago

    i love math...

    1st: x

    2nd: 3x (x is the first and 3 means 3 times larger)

    3rd: x+75 (first plus 75)

    so:

    x+ 3x + (x+75) = 180 (degrees used for a triangle, if you lay all the angles together, they'd make a straight line which is half the degrees of a circle)

    First you need to find the value for x

    x+3x+(x+75) = 180 //combine like terms, there are 5 x's

    5x + 75 = 180 //now subtract the number from answer

    -75 -75

    5x = 105 //now divide the 5 to leave the x on that side

    --- -----

    5 5

    x = 21

    so now you know x...go back and plug the x into the angles...

    1st: 21

    2nd: 3(21) = 63

    3rd: 21 + 75 = 96

    you can check all these by adding them together and they should equal 180(they do!)

    so the answer is ........the first angle.

    crap!! now I just realized you could've done that without all that wrok.....but here it is anyway.....just in case...

    all you really had to do was realize that the second angel is 3 times bigger than the first an dthe third angle is 75 more than the first....so both are bigger than the first which makes the first the smalles.....duh on my part....i just love working with the numbers so I didn't even try to really read it and work it in my head.

  • 1 decade ago

    Find the smallest angle (x):

    x + 3x + x + 75 = 180

    5x = 105

    x = 21

    Answer: 21°s is the smallest angle.

    Proof (sum of all angles is 360°s):

    = 21°s + 3(21°s ) + (21°s + 75°)

    = 21°s + 63°s + 96°s

    = 360°s

  • Anonymous
    1 decade ago

    Triangles have a total of 180 degrees...

    Given:

    1st angle = x

    2nd angle = 3x

    3rd angle = 75 + x

    x + 3x + 75 + x =180

    5x = 180 - 75

    5x = 105

    5x / 5 = 105 /5

    x = 21

    therefore the measure of the 1st angle is 21 degrees...

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  • 1 decade ago

    Let the1st angle = x

    let the second angle = 3x

    let the 3rd angle equals = x+75

    therefore,

    x+3x+x+75= 180

    5x=180-75

    5x= 105

    x = 21

    thus the smallest angle=x=21

    21 is the ans

    Source(s): ME
  • 1 decade ago

    Too easy - this is basic algebra.

    The total of the three angles of any triangle is 180 degrees. (75 + X) + 3X + X = 180

    5X + 75 = 180

    5X = 105

    X = 21

    The first angle = 21

    Second = 63

    Third = 96

  • 1 decade ago

    First angle: x

    Second angle: 3x

    Third angle: 75 + x

    first angle + second angle + third angle = 180

    x + 3x + 75 + x = 180

    5x = 105

    x = 21

    x is the smallest angle. Smallest angle = 21 degrees

  • Gili
    Lv 4
    1 decade ago

    Angles: x, y, z

    y = 3x

    z = 75 + x

    x + y + z = 180

    x + 3x + 75 + x = 180

    5x = 105

    x = 21

    y = 63

    z = 96

    The smallest angle is x = 21 degrees.

  • 1 decade ago

    Let F,S, and T be the first, second, and third angles.

    S = 3F

    T = F + 75

    F + S + T = 180

    F + 3F + (F + 75) = 180

    5F + 75 = 180

    5F = 105

    F = 21

    S = 3(21)

    S = 63

    T = (21) + 75

    T = 96

    F + S + T = 21 + 63 + 96 = 180

  • 1 decade ago

    1st angle = 21 degrees

    2nd angle = 63 degrees

    3rd angle = 96 degrees

    smallest measurement is 21 degrees.

  • Paige
    Lv 4
    4 years ago

    Let x = number of regular hats. Let y = number of large hats. We know that there are a total of 250 hats, so x + y = 250 The cost of the reg. hats is the number (x) times the price for each ($3.00) = 3x The cost of the large hats is the number (y) times the price for each ($7.00) = 7y The total cost is $1070. 3x + 7y = 1070 x + y = 250 so x = 250 - y. Put that in for x above. 3 (250 - y) + 7y = 1070 750 - 3y + 7y = 1070 750 + 4y = 1070 4y = 520 y = 130 = no. of large hats x = 250 - y = no. of reg. hats = 250 - 130 = 120

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