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Home > INT2 > Chapter 8 > Lesson 8.4.3 > Problem 8-106


Use the angle relationships in each of the diagrams below to solve for the given variables. Show all work.

The sum of the interior angles in an -gon can be found by calculating .

  1. A polygon with the following angles: 138 degrees, 106 degrees, m minus 9 degrees, m, 133 degrees, 120 degrees and m + 13 degrees.

  1. A pentagon with a line going through the interior from one side to an opposite vertex creating internally another pentagon and a triangle. For the triangle, the two external sides are equal with a 64 degree angle between them. The interior line creates a right angle with the adjacent right side. The next three angles clockwise are, 96, k, and 88 degrees. Thus all 5 angles of the external pentagon is labeled.

    Start by determining the measures of the base angles of the isosceles triangle.

  1. A pentagon where two of the sides are parallel. A third side is a transversal. The two same side interior angles of the transversal are unknown. A third angle, 135 degrees, is between the left parallel line and an interior line segment , A fourth angle, 3, y, is between the right parallel line and another interior line segment. Where the two interior line segments meet is a fifth angle, 2, y.

    The sum of the two unlabeled angles is . Why?