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EXTRA

Unit 30: Angle Problems

The SAT will test you on deriving angles based on shapes and other angles.

An Example:

In the figure above, what is the value of y?

A) 40
B) 45
C) 50
D) 60

Strategy:

  1. Find any opposite angles and mark them as congruent.
  2. Utilize the supplementary angle theorem with any angles that form a straight line.
  3. Look for polygons (usually they’ll be three-sided and four-sided shapes) and analyze the sums of their interior angles.
  4. If the problem identifies lines as parallel, utilize the rule for parallel lines cut by a transversal.

It may have been a few years since you had geometry.  Not to worry – there are only a few rules you need to remember to solve any angle problem.

1. Opposite Angle Theorem

This simply states that any time two lines cross, the angles opposite each other are the same.

2. Supplementary (and complementary) angles

You are most likely to see supplementary angles – angles that add up to 180°.      Complementary angles add up to 90°.

3. Parallel lines cut by another line (a transversal)

If parallel lines intersect another line (or lines), it creates angles that are the same.  So here:

Angles 1, 4, 5, and 8 are the same; angles 2, 3, 6, and 7 are the same.

4. Interior angles of a polygon

$$180(n-2)=total;of;interior;angles$$

The total number of degrees in the interior of a polygon can be calculated with the formula above, where n is the number of sides.  So,

A triangle has three sides.  (180(3-2)=180^circ) inside a triangle.

A quadrilateral has four sides.  (180(4-2)=360^circ)

A pentagon has five sides.  (180(5-2)=540^circ)

You need to memorize this formula!