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Home > INT2 > Chapter 6 > Lesson 6.1.3 > Problem 6-33

6-33.

Use the relationships found in each of the diagrams below to solve for and . Assume the diagrams are not drawn to scale. State which geometric relationships you used.

  1. Two triangles connected at a single vertex by extending two sides of the first and enclosing the second by a line segment. The triangle at the left has angles 70 degrees and 41 degrees. The triangle at the right has 58 degrees and x degrees. At the common vertex, the angle at the intersection of the segments, outside both triangles, is y.

    What is the measure of the missing angle in the left triangle? Once you know that angle, calculate the measure of angle .

    ;
    Triangle Angle Sum Theorem and ____

  1. 3 segments form a z shape, a fourth segment connects the center segment of the z, with the right end of the bottom segment, creating a triangle, top & bottom segments, each marked with 1 arrow, inside the z, top angle is labeled, x, & bottom angle is labeled 47 degrees, bottom right angle of triangle is labeled 32 degrees, the angle right of center segment & above fourth segment, is labeled y.

    Parallel lines create alternate interior angles. Which angles are alternate interior angles in this diagram?

  1. 2 transversal lines, 1 at the top & 1 at the bottom, crosses 2 downward slanting parallel lines. The intersection of these lines in degrees: the top transversal & the far left parallel line: the exterior top angle is 83. The top transversal & the far right parallel line: the exterior bottom angle is y. The bottom transversal & the far left parallel line: the exterior top angle is x. The bottom transversal & the far right parallel line: the exterior top angle is 127.

    Redraw the diagram with only the parallel lines and the line at the top. Then determine the value of .

  1. A triangle with side lengths of 3 on left side, x on right side and y on bottom side. 45 degrees angle is in between the left side and right side. Another 45 degrees angle between the bottom side and right side.

    This diagram is not drawn to scale. Determine the measure of the missing angle then draw the diagram to scale. What special triangle is this?

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