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Examine the geometric relationships in each of the diagrams below. For each one, write an equation and solve for the value of the variable. Name all geometric relationships or theorems that you use.

  1. Two adjacent angles together, form a 90 degree angle. The angle on the left is, 4 X minus 2 degrees. The angle on the right is, X.

    What is the sum of the two angles?

    (complementary angles)

  1. A triangle with labeled interior angles: top angle is 2 M + 3 degrees, lower left angle is M + 9 degrees, and lower right angle M minus 1 degrees.

    The interior angles of a triangle add up to how many degrees?

  1. 2 intersecting lines. About the point of intersection, opposite angles are 3 K, +, 18 degrees, and 7 K minus 6 degrees.

    What is true about the measures of vertical angles?

  1. A triangle has an internal line segment parallel to the left side and stretching between the other two sides.  The two triangles share a common vertex. The diagonal side of the original triangle is 16, but, x, for the internal triangle. The base of the original triangle is 13, but, 8, for the internal triangle.

    These are similar triangles, so write a proportion using the ratios of the corresponding sides.