McGraw-Hill Education GRE 2019

(singke) #1
Since x, y, and z lie on a line, they are supplementary: x + y + z = 180.
Substitute 80 for x:
80 + y + z = 180
y + z = 100


  1. A Since angles a, b, and c lie on a line, a + b + c = 180. If a is the largest of the
    three values, then a must be greater than 60. To understand why, think of what
    would happen when a = 60. If a = 60 and b and c are smaller than a, then the
    sum of the three angles cannot be 180. Thus a > 60.

  2. C Since b is a straight line, the five angles above a must add to 180: 4x + y = 180.
    Since x + y = 75, you can use substitution to solve for x: y = 75 – x. Substitute
    (75 – x) for y in the first equation:
    4 x + (75 – x) = 180
    3 x = 105
    x = 35
    If x = 35, then y = 40. Now solve for q. Since a is a straight line, x + q = 180.
    x = 35, so q = 180 – 35 = 145. q – y = 145 – 40 = 105.

  3. C Since l and m are perpendicular, all the angles formed at the intersection
    of l and m must equal 90 degrees. Thus a + b = 90. Substitute 3b for a to solve
    for b:
    3 b + b = 90
    4 b = 90
    b = 22.5

    a = 90 – 22.5 = 67.5
    Thus a – b = 67.5 – 22.5 = 45.

  4. D Since b is a large angle created by the transversal and c is the small angle
    created by the transversal, b + c = 180. Substitute 100 for b:
    100 + c = 180
    c = 80

  5. A Since l and k are parallel lines cut by a transversal, the sum of the smaller
    and larger angles must equal 180. Thus a + d = 180. Substitute d + 30 for a:
    (d + 30) + d = 180
    2 d + 30 = 180
    2 d = 150
    d = 75


374 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 374 12/05/17 12:04 pm

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