McGraw-Hill Education GRE 2019

Intersecting Lines and Vertical Angles

The intersection of two lines will always create four angles.

A D

C B

130°

130°

50° 50°

These angles have two properties:

1. They will add up to 360.


2. The angles opposite each other will be equal. These angles are termed
   vertical angles.

80°

2 y°

x°

Note: Figure not drawn to scale.

What is the value of x in the figure above?

SOLUTION: Since x and 2y lie on the same line, x + 2y = 180. The angle vertical

to 2y = 80, so you can substitute 80 for 2y in the equation and solve: x + 80 =

180 → x = 100.

Note that the two preceding properties can apply to situations in which more than

two lines intersect. Here is the more general form of Property 1: the angles around a

point must add up to 360.

a° b°

d°

a + b + c + d + e + f = 360

e°

c°

f°

Since these angles are all around a point, a + b + c + d + e + f = 360. In addition,

a = f, b = e, c = d. Finally, a, b, and c are supplementary, and d, e, and f are

supplementary.

Parallel Lines and Transversals

Parallel lines by definition will never intersect. On the GRE, you will be expected

to understand the relationships among the angles of parallel lines cut by a

transversal.

CHAPTER 13 ■ GEOMETRY 367

04-GRE-Test-2018_313-462.indd 367 12/05/17 12:04 pm