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20 August, 05:13

The measure of the second angle (y) of a triangle is 44° more than that of the first angle (x), and the third angle

(z) is 28° less than twice the second angle. Find the measures of all three angles.

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  1. 20 August, 08:28
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    x = 19, y = 63, z = 98

    Step-by-step explanation:

    the three angles of a triangle add to 180 degrees

    x+y+z = 180

    The measure of the second angle (y) of a triangle is 44° more than that of the first angle (x)

    y = 44+x

    the third angle (z) is 28° less than twice the second angle y

    z = 2y-28

    substitute 2y-28 into x+y+z = 180

    x + y + z=180

    x + y + (2y-28) = 180

    combine like terms

    x + 3y - 28 = 180

    now y = 44+x substitute this into the above equation

    x + 3 (44+x) - 28 = 180

    distribute

    x + 132 + 3x - 28 = 180

    combine like terms

    4x + 104 = 180

    subtract 104 from each side

    4x + 104-104 = 180-104

    4x = 76

    divide by 4

    4x/4 = 76/4

    x = 19

    now lets find y

    y = 44+x

    y = 44+19

    y = 63

    and we need to find z

    z = 2y-28

    z = 2 * (63) - 28

    z = 126 - 28

    z=98
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