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
- 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. - 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. - 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. - 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 - 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