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Home > CCG > Chapter 6 > Lesson 6.2.3 > Problem 6-74


For each diagram below, use geometric relationships to solve for the given variable(s). Check your answer.

  1. Two adjacent angles together, form a 90 degree angle. The angle on the left is, 18 X, minus, 10, degrees. The angle on the right is, 7 X, degrees.

    The angle that is and the angle are complementary.
    Complementary means the angles add up to _____

  1. A triangle has two sides with 1 tick mark.  The angle between the two sides has one side extended forming an exterior angle, 110 degrees.  Another angle, x, is opposite a side with a tick mark.

    Adjacent angle pairs that form a straight line are supplementary and base angles of an isosceles triangle are equal.

  1. A transversal line,  cuts two horizontal parallel lines. About the point of intersection, of the top parallel line, and the transversal line is the interior, left angle, 5 X, +, 2, degrees. About the point of intersection, of the bottom parallel line, and the transversal line, are the interior left angle, 63 degrees, and the interior right angle, 3 Y, minus, 12 degrees.

    First solve for , then solve for .

  1. A triangle with two side lengths of 3, X + 13. Opposite each of those two sides is a 40 degree angle. The base is labeled, y.

    Since the triangle is isosceles, start by solving for .
    Next, solve for the unknown interior angle.
    Then use the Law of Sines to solve for .

    Refer to the Math Notes box in Lesson 5.3.2 if you need help remembering the Law of Sines.