Here’s an example.
12.
Lines l and m extend from two sides of the regular hexagon as shown above. If A = 120,
what is the value of B, in degrees?
A) 30
B) 60
C) 90
D) 140Here’s How to Crack It
Sometimes, Ballparking can even help on geometry questions. Not all pictures are drawn to scale, so
don’t assume the figure is exact. You can, however, use what the question tells you about the figure to
estimate angles, line lengths, areas, and points on graphs in the xy-plane.
If this picture is drawn to scale, the angle with measurement B looks to be acute, making (A) or (B) a
good bet. The question says the hexagon is “regular,” which means that all the interior angles have the
same measure, and the drawing looks like this is the case. Start by marking the angle that is A° as 120° on
the figure. This angle looks like 120°, so B can’t possibly equal 90° or 140°. Eliminate (C) and (D). To
find the exact value of B, you need to find the measure of the angle opposite it, which is one of the angles
from the triangle. The angle of the upper left corner of the triangle is formed by drawing a straight line
from the angle that is A°, or 120°. There are 180° in a straight line, so the upper left corner of the triangle
measures 180 – 120 = 60°. Label that on the figure as well. The fact that the hexagon is a regular one
means that all the interior angles are 120°, so label the one next to the bottom corner of the triangle. Since
this corner of the triangle is formed in the same way as the upper left corner, the bottom corner also
measures 60°. Label that. There are 180° in a triangle, so the upper right angle is also 60°. The angle
measuring B° is opposite this, so B is 60° and (B) is correct.