Session 4, Part B:
Angles in Polygons

In This Part: Classifying by Measure | Other Classifications | Measuring Angles
Sums of Angles in Polygons

 Another way to classify angles is by their relationship to other angles. As you work on the types of classifications in Problems B4 and B5, think about the key relationships between angles. The types of angles you will be looking at in Problems B4 and B5 are easily shown on two parallel lines cut by a transversal. You can use several copies of the same polygon and place them together to form parallel lines that are cut by a transversal.

Problem B4

Use two or more polygons to illustrate the angles below:

 a. Supplementary angles (the sum of their measures equals 180 degrees) b. Complementary angles (the sum of their measures equals 90 degrees) c. Congruent angles (their angle measurement is the same) d. Adjacent angles (they share a common vertex and side)

Problem B5

Use two or more polygons to illustrate the angles below, and explain how you would justify that some of the angles are congruent:

 a. Vertical angles (the angles formed when two lines intersect; in the figure above, ad, cb, eh, and fg are pairs of vertical angles, and the angle measures in each pair are equal) b. Corresponding angles (the angles formed when a transversal cuts two parallel lines; in the figure above, ae, bf, cg, and dh are pairs of corresponding angles, and the angle measures in each pair are equal) c. Alternate interior angles (the angles formed when a transversal cuts two parallel lines; in the figure above, cf and de are pairs of alternate interior angles, and the angle measures in each pair are equal)

Problem B6

Find one or more polygons you can use to see examples of the following angles:

 a. Central angles (for regular polygons, the central angle has its vertex at the center of the polygon, and its rays go through any two adjacent vertices) b. Interior or vertex angles (an angle inside a polygon that lies between two sides) c. Exterior angles (an angle outside a polygon that lies between one side and the extension of its adjacent side):

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