In a triangle, the angles are u°, v° and w°.?

In a triangle, the angles are u°, v° and w°. Determine the angles of the triangle if v is half the size of w and if u is the mean of v and w.

My book say that the answer are:

u=60°

v=40°

w=80°

But I dont know how to solve the problem, can someone help me?

3 Answers

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  • 2 months ago
    Favorite Answer

    If v is half of w:

    v = w/2

    and u is the mean of v and w:

    u = (v + w) / 2

    And you know it's a triangle, the sum must be 180:

    u + v + w = 180

    We now have a system of three equations and three unknowns that we can solve.

    Let's first substitute the expression for u in terms of v and w into from the second equation into the third:

    (v + w) / 2 + v + w = 180

    Let's multiply both sides by 2 to simplify:

    v + w + 2v + 2w = 360

    3v + 3w = 360

    Divide both sides by 3:

    v + w = 120

    The first equation is v in terms of w, so substitute that into this equation and solve for w:

    w/2 + w = 120

    Again, multiply both sides by 2:

    w + 2w = 240

    3w = 240

    w = 80

    Now that we have w we can solve for v and u:

    v + w = 120

    v + 80 = 120

    v = 40

    u = (v + w) / 2

    u = (40 + 80) / 2

    u = 120 / 2

    u = 60

    Your solution us:

    u = 60, v = 40, w = 80

  • sepia
    Lv 7
    2 months ago

    In a triangle, the angles are u°, v° and w°.

    Determine the angles of the triangle,

    if v is half the size of w and if u is the mean of v and w.

    u + v + w = 180°

    (v + w)/2 + w/2 + w = 180°

    v + 4w = 360°

    3w - u = 180° = u + v + w

    2w - 2u - v = 0

    Solution:

    u = 60°, v = 40°, w = 80°

  • JOHN
    Lv 7
    2 months ago

    Call the angles 2x, 4x, (2x + 4x)/2 = 3x

    2x + 4x + 3x = 9x = 180°, x = 20.

    The angles are: 40°, 80°, 60°.

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