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Home > GC > Chapter 3 > Lesson 3.2.3 > Problem 3-70


Use the relationships in each diagram below to solve for . Justify your solution by stating which geometry relationships you used.  

  1. A quadrilateral with two parallel sides. A diagonal from the top left to bottom right divides the figure into 2 triangles. The given angles in the bottom triangle are lower left, 71 degrees, upper left, x degrees.  The top triangle has 1 given angle at the top left, 58 degrees.  The two angles x and 58 are adjacent angles.

    Parallel lines cut by a transversal creates equal angles.Which angles in the figure are equal?

  1. Four angles about a point of intersection. The angles starting at top left going clockwise and are labeled as follows: x, 84 degrees, 3 x + 14 degrees, and 90 degrees.

    Think of the angle measure of a circle. How can you use that measure to solve for ?

  1. Right triangles with the following leg lengths: height, x, base, square root of 3, and hypotenuse is 2.

    Use the Pythagorean Theorem. Remember to justify all your work with the relationships you used!