After the jump is a review of some terms and concepts that you must know in order to deal with angles on the SAT and other standardized tests. This post also runs through four typical problems that require you to apply these concepts.
Vocabulary Review
supplementary – the angles add up to 180 degrees.
e.g. Angles x and y are supplementary. If angle x is 56 degrees, what is the measure of angle y?
- ans: y = 180 – 56 = 124 degrees.
linear pair – two angles that are next to each other on a straight line; are always supplementary.
complementary – the angles add up to 90 degrees.
e.g. Angles x and y are complementary. If angle y is 73 degrees, what is the measure of angle x?
- ans: x = 90 – 73 = 17 degrees
vertical – the angles are opposite each other; are congruent.
alternate interior angles – angles found between two parallel lines on opposite sides of a third line that intersects these parallel lines (transversal); are congruent.
alternate exterior angles – angles found outside two parallel lines that are on opposite sides of the transversal; are congruent.
corresponding angles – angles on the same side of the transversal; one is outside and one is inside; are also congruent.
midpoint – the exact middle of a line segment.
e.g. C is the midpoint of AB. If AC is equal to 4, what is the length of AB?
- ans: AC and CB are equal in measure because C is the midpoint. Therefore, AB is equal to 8.
bisect – to cut into two equal halves. If a 84 degree angle is bisected, that means a line is drawn through the angle that splits it into two 42 degree angles.
Example Problems
A Problem Involving a Linear Pair
A Problem Involving Vertical Angles
A Problem Involving Parallel Lines
A Problem Involving Midpoint
