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Home > GC > Chapter 6 > Lesson 6.2.5 > Problem 6-85

6-85.

For each shape below, use the geometric relationships to solve for the given variable(s). Show all work. Name the geometric relationships you used.

  1. A triangle with three labeled interior angles: top angle is 4 X + 28 degrees, lower left angle is X + 19 degrees, and lower right angle is 3 X + 13 degrees.

    What is the sum of the angles within a triangle?

    , Triangle Angle Sum

  1. A triangle with side lengths 6, K + 3 and 3  K + 18.

    What do the tick marks on the sides of the triangles mean?

    , Isosceles triangle

  1. A parallelogram with three labeled angles: upper left angle is 4, T + 13 degrees, lower left angle is W, and lower right angle is 8, T minus 23 degrees.

    Extend the parallel sides.

    Parallel lines have same side interior supplementary angles.

    By the Equal Values Method:

    Parallel lines

  1. A triangle with side lengths 43 on left side, 43 on bottom side, X on right side. 71 degrees angle is in between the 43 sides.

    Use the Law of Cosines to solve for the unknown side.