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Home > GC > Chapter 11 > Lesson 11.1.1 > Problem 11-10

11-10.

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 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 intercepted arc is twice 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 .

  1. A triangle with sides labeled: left, x, right, y, bottom, 9. Angles labeled: top, 73 degrees, bottom right, 57 degrees.

    Use the Law of Sines.

    ,

  1. A triangle with left and right side, each with one tick mark. Angles labeled: top, 4 X minus 2 degrees, left, 8 X minus 9 degrees.

    Use the Triangle Angle Sum Theorem.