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Home > CC2 > Chapter Ch9 > Lesson 9.1.2 > Problem 9-34

9-34.

For each diagram below, identify each set of angles as complementary, supplementary, or vertical. Then use what you know about the properties of angles to find the measure of each angle labeled with a variable.  

  1. 3 rays start at the same point, left ray is vertical, middle ray goes up and to the right, right ray is horizontal. Gaps between rays labeled as follows: left and middle, 68 degrees, middle and right, a.

    Write an equation relating and .

    Subtract from both sides.

    ; they are complementary angles

  1. 3 rays start at the same point, left ray is horizontal, middle ray goes up and to the left, right ray is horizontal. Gaps between rays labeled as follows: left and middle, 36 degrees, middle and right, b.

    These angles are supplementary, so . What is the measure of ?

  1. Two intersecting lines, with the following angles labeled, clockwise about the point of intersection: 66 degrees, c degrees, e degrees, and d degrees.

    e and are vertical angles, so they are equal in measure. and are also vertical angles.

    Angle is . Use this to help you find and .

  1. 3 rays start at the same point, left ray is vertical, middle ray goes up and to the right, right ray is horizontal. Gaps between rays labeled as follows: left and middle, 60 degrees, middle and right, x.

    Use part (a) to help you solve this problem.

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