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Home > GC > Chapter 7 > Lesson 7.1.3 > Problem 7-33


Examine the relationships in the diagrams below. For each one, write an equation and solve for the given variable(s). Show all work.  

  1. A triangle with 2 sides marked with one tick mark. Angles opposite each side with a tick mark are, 6, n minus 3 degrees and n + 17 degrees,

    Since the triangle is isosceles, the angles shown are equal.

  1. Figure 1: A transversal line cuts two parallel lines. About the point of intersection, of the left parallel line and the transversal line is the interior right angle, 7 X minus 19 degrees, and the exterior left angle, 5 Y minus 2 degrees. About the point of intersection, of the right parallel line and the transversal, is the interior left angle, 3 X, +, 14 degrees.

    First solve for , then . Refer to the Math Notes box in Lesson 2.1.4 if you need help remembering any specific angle pair relationships.

  1. A parallelogram with the top and bottom sides marked with two tick marks and the left and right sides marked with one tick mark. The upper left vertex angle is 5 W + 36 degrees. The lower left vertex angle is 3 W.

    Same side interior angles are supplementary.

  1. A triangle with the following side lengths 15, 25, and K. 120 degrees is opposite the side, K.

    Use the Law of Cosines to solve for .