Math IC questions covering parallel lines cut by a transversal are usually straightforward. For example:
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In the figure below, if lines m and n are parallel and  = 110º, then f – g = |
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If you know the relationships of the angles formed by two parallel lines cut by a transversal, answering this question is easy.
and
are alternate exterior angles, so
.
is adjacent to
, so it must be equal to 180º – 110º = 70º. From here, it’s easy to calculate that
f – g = 110º – 70º = 40º.
Perpendicular Lines
Two lines that intersect to form a right (90º) angle are called perpendicular lines. Line segments AB and CD are perpendicular.
A line or line segment is called a perpendicular bisector when it intersects a line segment at the midpoint, forming vertical angles of 90º in the process. For example, in the figure above, since AD = DB, CD is the perpendicular bisector of AB.
Keep in mind that if a single line or line segment is perpendicular to two different lines or line segments, then those two lines or line segments are parallel. This is actually just another example of parallel lines being cut by a transversal (in this case, the transversal is perpendicular to the parallel lines), but it is a common situation when dealing with polygons. We’ll examine this type of case later.
