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Home > CCAA > Chapter 8 Unit 7 > Lesson CC2: 8.3.3 > Problem 8-90

8-90.

Find the value of each variable in the following figures. Do not use a protractor. Use the properties of angles to help you.  

  1. 3 rays have the same starting point, left ray is horizontal, right ray is vertical, middle ray slants up and left, with the gap between the rays, labeled as follows: left and middle, 37 degrees, middle and right, a.

    . Solve for .

  1. 3 rays have the same starting point, left ray is horizontal, middle ray slants up and left, right ray is horizontal, with gap between rays, labeled as follows: left and middle, 85 degrees, middle and right, b.

     

    These angles are supplementary.

  1. Two lines intersect at a point creating 4 angles about the point of intersection, with angles labeled as follows: Left, 47 degrees. Right, c.

    and are vertical angles. What does that tell you about the measure of angle ?

  1. 3 rays have the same starting point, left ray is horizontal, middle ray slants down and to the right, right ray is horizontal, with the gap between the rays labeled as follows: left and middle, 137 degrees, middle and right, d.

     
     

    Set up an equation relating and . .

    Subtract from both sides.

  1. 3 rays have the same starting point, left ray is vertical, middle ray slants to the right and up, right ray is horizontal, with gap between the rays, labeled as follows: left and middle, e, middle and right, 15 degrees.

    and are complementary angles, meaning their sum is .

  1. Two lines intersect at a point, creating 4 angles, about the point of intersection, labeled as follows: top,153 degrees, right, I, bottom, f.

    and are vertical angles, and and are supplementary.

    ,

  1. 3 rays have the same starting point, left ray is down and to the left, middle ray is down and to the right, right ray is up and to the right in the same line as the left ray, with gaps between the rays, labeled as follows: left and middle, 115 degrees, middle and right, g.

     

    . Refer to part (d) for the steps to solving this problem.

  1. 3 rays have the same starting point, left ray is horizontal, middle ray goes up and to the left, right ray is horizontal, with gaps between the rays labeled as follows: left and middle, 95 degrees, middle and right, h.

     
     

    . Now solve for the value of .

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