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Home > CCG > Chapter 7 > Lesson 7.1.2 > Problem 7-18

7-18.

Examine the geometric relationships in each of the diagrams below. For each one, write and solve an equation to find the value of the variable. Name any geometric property or conjecture that you used.  

  1. An angle divided into three equal angles.  The  angle on the left is labeled m. The middle angle is labeled 5 m minus 28 degrees.

    How do the different measures of the angle relate to each other? How can you use this to solve for ?

  1. A parallelogram with the left bottom angle labeled 3 x + 38 degrees and the right bottom angle labeled 7 x minus 8 degrees.

  1. below is equilateral.
    Equilateral triangle A, B, C. Side A, B is 3, n minus 1. A line segment is drawn from the upper vertex, A, perpendicular to the base.   The left side of B, C, to the right angle is labeled, n = 4.

    How do each of the sides of the triangle relate to each other if the triangle is equilateral?
    How can that help you solve for ?

  1. is the center of the circle below and

    A circle with center C. Line A B is the diameter and line C D is the radius.

    How do and relate to each other?