McGraw-Hill Education GRE 2019

x°

x°

y°

x° y°

y°

y° x°

The best way to think about the relationship among the angles is in terms of the

small angles and the large angles. All of the smaller angles will be acute (less than

90 degrees), and all of the larger angles will be obtuse (greater than 90 degrees).

All the smaller angles will have the same measure, and all of the larger angles will

have the same measure. Thus in the preceding diagram, x < 90, and y > 90. Finally,

the sum of any small angle and any large angle will always be 180. Thus x + y = 180.

Understanding and implementing these properties will equip you well on most

questions that test parallel lines and transversals.

l°

m°

A

CD

B

In the diagram above, lines AB and CD are parallel. If the ratio of l to m is 3

to 2, what is l?

SOLUTION: When two parallel lines are cut by a transversal, the sum of the

small and large angles is 180. Thus l + m = 180. Since ml =^32 , you can let l = 3x

and let m = 2x. Substitute these terms into the first equation:

l + m = 180

↓

3 x + 2x = 180

5 x = 180

x = 36 and l = 3x, so l = 3(36) = 108.

368 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 368 12/05/17 12:04 pm