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Home > INT2 > Chapter 12 > Lesson 12.2.3 > Problem 12-114


For each of the relationships represented in the diagrams below, write and solve an equation for and/or . Justify your method. In part (a), assume that is the center of the circle.

  1. Circle with center, C, with a diameter, a radius, and a chord, connecting the ends of the radius and one end of the diameter. The inscribed angle, between the diameter and chord, is labeled, x, and the minor arc, contained between the ends of the chord, is labeled, 106 degrees.

    Added labels to the circle, Endpoints of diameter, A, and, D, endpoints of chord, B, and, D.

     because  is a diameter

    The measure of the intercepted arc is twice the measure of the inscribed angle

    One equation could be 

  1. 4 sided polygon, with top and bottom sides marked with one arrow each, with interior angles labeled as follows: upper left, x, upper right, 5 Y,  lower right, 3 Y minus 16 degrees, lower left, 67 degrees.

    Which angles are supplementary? This will help you write equations to solve for and .